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ABSTRACT

YOTAKHONG, PURK. Flexural Performance of MMFX Reinforcing Rebars in Concrete Structures. (Under the direction of Dr. Sami Rizkalla)

Use of Micro-composite Multi-structural Formable Steel, commercially known as

“MMFX”, as a replacement for convention steel is gaining popularity in many concrete

structures. The high-corrosive resistance nature and high-strength characteristics of the

MMFX rebars could provide additional service life to concrete structures in areas that are

prone to severe environmental conditions. The research program presented in this thesis was

designed to study the flexural behavior of rectangular concrete beams reinforced by MMFX

rebars.

This thesis presents the experimental program carried out at the Constructed

Facility Laboratory (CFL), North Carolina State University, to test a total of four large-scale

concrete beams. All beams were 16 feet long, 12 inches wide, and 18 inches high. Three

beams were reinforced by MMFX rebars in the tension side, and one beam was reinforced by

conventional steel rebars in the tension side. All beams were equally reinforced by

conventional steel rebars on the compression side. Three beams were tested under static

loading conditions, while the remaining MMFX reinforcing beam was tested under a slow

cyclic loading condition. All beams were tested to failure in order to investigate the behavior

during the pre-cracking, cracking, post-cracking, ultimate capacities, and modes of failure.

All MMFX reinforced concrete beams experienced higher ultimate strength and a

comparable amount of ductility in comparison to this control beam. The failure mode of all

beams was classified as ductile flexural failure due to significant straining of the tension

reinforcement preceding the crushing of the concrete. No bond or other types of failure was

observed during the time of testing. The design recommendations and guidelines are

proposed based on the results from this investigation and additional parametric study. Based

on the research findings, the minimum and maximum reinforcement ratio has been identified

as well as the optimal use of MMFX as reinforcement for concrete structures.

FLEXURAL PERFORMANCE OF MMFX REINFORCING REBARS IN

CONCRETE STRUCTURES

by

PURK YOTAKHONG

A thesis submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Master of Science

CIVIL, CONSTRUCTION, AND ENVIRONMENTAL ENGINEERING

Raleigh

November 25, 2003

APPROVED BY:

(Chair of Advisor Committee)

ii

DEDICATION

The author would like to dedicate this thesis to my parents,

Suchit and Dr. Somchit Yotakhong, who made everything possible.

iii

BIOGRAPHICAL INFORMATION

The author was born in Bangkok, Thailand in 1979 and moved to United States of

America in 1996. He received his Bachelor’s degree in Civil Engineering from The

University of Alabama in May 2001. He is an active member in Chi Epsilon, Golden Key,

Gamma Betha Phi honor societies.

iv

ACKNOWLEDGEMENTS

The author wishes to express his greatest gratitude to his supervising professor, Dr.

Sami H. Rizkalla, for his unparallel guidance, patience, and support. The author also would

like to thank Dr. Emmett A. Sumner and Dr. Mervyn J. Kowalsky for serving on the author’s

thesis committee.

In addition, the author wishes to express his sincere thanks to Dr. Raafat El-Hacha for

his technical, experimental, and analytical assistance throughout the length of this research.

The technical assistance given by Jerry Atkinson, Matt Vorys, William Dunleavy,

Hossam El-Agroudy, and José Neres da Silva Filho during the experimental work is also

greatly appreciated. Special thanks go to all graduate students at the Construction Facility

Laboratory for their help during the fabrication and testing process. Much appreciation also

goes to my friends, Daniel Mitchell and David Jordan, who provided help during the writing

process.

Finally, the author wishes to express his deeply felt gratitude to his family who made

all this possible. The immeasurable support, patience, and guidance from my father,

Dr. Somchit Yotakhong, my mother, Suchit Yotakhong, and my sister, Panan Yotakhong,

cannot be praised enough. Lastly, the author would like to thank Miss Vanida Vatcharanukul

for her endless inspiration.

v

TABLE OF CONTENTS

LIST OF TABLES.................................................................................................................ix

LIST OF FIGURES ...............................................................................................................x

NOTATIONS.........................................................................................................................xiii

CHAPTER 1: INTRODUCTION ..............................................................................1

1.1 GENERAL..............................................................................................1

1.2 OBJECTIVE ...........................................................................................2

1.3 SCOPE ....................................................................................................2

CHAPTER 2: LITERATURE REVIEW ...................................................................4

2.1 GENERAL..............................................................................................4

2.2 DEFINITION OF MMFX.......................................................................6

2.3 MATERIAL CHARACTERISTIC OF MMFX .....................................7

2.3.1 Corrosion Resistance .................................................8

2.3.2 Strength Parameters ...................................................8

2.3.3 Fatigue .......................................................................9

2.3.4 Toughness ..................................................................10

2.3.5 Brittleness ..................................................................10

2.4 REINFORCEING CONCRETE EVALUATION ..................................10

2.5 FIELD APPLICATIONS........................................................................13

2.6 FLEXURAL BEHAVIOR OF CONCRETE BEAMS

REINFORCED BY MMFX REBAR ............................................................14

CHAPTER 3: EXPERIMENTAL PROGRAM.........................................................25

3.1 GENERAL...............................................................................................25

3.2 TEST SPECIMENS................................................................................26

vi

3.2.1 Design of the Specimens............................................26

3.2.2 Flexural Reinforcement .............................................27

3.2.3 Shear Reinforcement..................................................27

3.3 MATERIAL PROPERTIES ...................................................................28

3.3.1 Concrete .....................................................................28

3.3.2 Steel ...........................................................................30

3.4 FABRICATION OF THE SPECIMENS................................................31

3.5 INSTRUMENTATION ..........................................................................32

3.6 TESTING PROCEDURE .......................................................................33

3.6.1 Test Setup ..................................................................33

3.6.2 Preparation for Testing ..............................................34

3.6.3 Testing .......................................................................34

CHAPTER 4: EXPERIMENTAL RESULTS ...........................................................44

4.1 GENERAL...............................................................................................44

4.2 MATERIAL PROPERTIES ....................................................................44

4.2.1 Concrete ........................................................................44

4.2.1.1 Compressive Strength ...................................44

4.2.1.2 Tensile Strength ............................................45

4.2.2 Steel ..............................................................................46

4.2.2.1 Compression Reinforcement.........................46

4.2.2.2 Tension Reinforcement.................................46

4.3 BEHAVIOR OF BEAM B1....................................................................48

4.3.1 Flexural Behavior ......................................................48

4.3.2 Crack Pattern..............................................................49

4.3.3 Crack Width ...............................................................50

4.3.4 Deflection...................................................................50

4.3.5 Ultimate Flexural Capacity and Failure Mode ..........51



vii

4.4.2 Crack Pattern..............................................................53

4.4.3 Crack Width ...............................................................54

4.4.4 Deflection...................................................................54




4.5.2 Crack Pattern..............................................................58

4.5.3 Crack Width ...............................................................58

4.5.4 Deflection...................................................................59




4.6.2 Crack Pattern..............................................................63

4.6.3 Crack Width ...............................................................63

4.6.4 Deflection...................................................................64


CHAPTER 5: DISCUSSION OF EXPERIMENTAL RESULTS AND

ANALYTICAL PREDICTION .................................................................................85

5.1 GENERAL.............................................................................................85

5.2 FLEXURAL BEHAVIOR ......................................................................85

5.2.1 Beam B1 vs. Beam B2 ...............................................86

5.2.2 Beam B2 vs. Beam B3 ...............................................87

5.2.3 Beam B3 vs. Beam B4 ...............................................89

5.3 CRACK INFORMATION......................................................................91

5.4 FAILURE MODE...................................................................................92

5.5 SERVICABILITY ..................................................................................94

5.5.1 Deflection....................................................................94

5.5.2 Crack Width ...............................................................95

5.6 FLEXURAL ANALYSIS.......................................................................95

viii

5.6.1 Cracking Moment Calculation...................................99

5.6.2 Failure Criteria ...........................................................99

5.7 MATERIAL MODELING......................................................................100

5.7.1 Concrete .....................................................................100

5.7.2 Compression Reinforcement......................................101

5.7.3 Tension Reinforcement..............................................102

5.8 DEFLECTION PREDICTION ...............................................................103

5.9 VERIFICATION OF ANALYTICAL MODEL.....................................104

5.9.1 Grade 60 Beam .........................................................104

5.9.2 MMFX Beam ............................................................105

5.10 MODIFIED MMFX MODEL...............................................................106

5.10.1 Response of Beams Based on the Modified MMFX

Characteristic .............................................................106

5.11 PARAMETRIC STUDY ......................................................................107

5.11.1 Results and Discussion of Parametric Study .............109

CHAPTER 6: SUMMARY AND CONCLUSION...................................................139

6.1 Summary ...............................................................................................139

6.2 Conclusion ............................................................................................139

6.3 Recommendation for Future Students ..................................................142

CHAPTER 7: REFERENCES...................................................................................143

ix

LIST OF TABLES

TABLE

2.1 Product evaluation table .................................................................................................21

3.1 Experimental test matrix .................................................................................................36

3.2 Summary of location, and function of each device.........................................................36

3.3 Testing program on Beam B4 .........................................................................................36

4.1 Compressive strength of the concrete .............................................................................67

4.2 Tensile strength of the concrete ......................................................................................67

4.3 Results from tension test of reinforcements ...................................................................68

5.1 Summary of test results...................................................................................................113

5.2 Summary of parametric study.........................................................................................114

x

LIST OF FIGURES

FIGURES

2.1 Accelerated Chloride Threshold (ACT) test of MMFX steel .......................................22

2.2 Typical stress-strain curve of MMFX, and Grade 60 steel in tension ..........................22

2.3 Typical fatigue limit of MMFX, and Grade 60 steel ....................................................23

2.4 Typical Brittle fracture data of MMFX, and Grade 60 steel ........................................23

2.5 Field application of MMFX steel..................................................................................24

2.6 Load-deflection behavior by Marcus H. Ansley...........................................................24

3.1 Typical reinforcement for Beam B1, B3, and B4 .........................................................37

3.2 Stirrup details for all beams ..........................................................................................37

3.3 Typical distribution of shear reinforcement..................................................................38

3.4 Setup for concrete compression strength test ...............................................................39

3.5 Type of compression failure on the tested cylinder ......................................................39

3.6 Type of tensile failure on the tested cylinder................................................................39

3.7 Test setup for tension test .............................................................................................40

3.8 Type of tension failure on the tested rebar ...................................................................40

3.9 Steel cage and form.......................................................................................................41

3.10 Casting and finishing of the specimen..........................................................................41

3.11 Curing of the beam........................................................................................................41

3.12 Test setup and instrumentation .....................................................................................42

3.13 Typical beam setup .......................................................................................................43

4.1 Stress-strain relationship for concrete ..........................................................................69

4.2 Stress-strain relationship for #4 Grade 60 compression reinforcement........................69

4.3 Stress-strain relationship for #6 Grade 60 and MMFX tension reinforcement ............70

4.4 Initial stage of loading on Beam B1 .............................................................................70

4.5 Crushing of the concrete on Beam B1 ..........................................................................71

4.6 Crack pattern on Beam B1............................................................................................71

4.7 Load-crack width information of Beam B1 ..................................................................72

4.8 Load-midspan deflection of Beam B1 ..........................................................................72

xi

4.9 Load-steel strain of Beam B1 .......................................................................................73

4.10 Load-concrete strain of Beam B1 .................................................................................73

4.11 Initial stage of cracking of Beam B2 ............................................................................74

4.12 Initiation of crushing of concrete of Beam B2 .............................................................74

4.13 Failure mode of Beam B2 due to crushing of concrete ................................................75


4.15 Load-crack width of Beam B2......................................................................................76




4.19 Initial stage of cracking on Beam B3............................................................................78


4.21 Failure mode of Beam B3 .............................................................................................79





4.26 Initial stage of cracking on Beam B4............................................................................81

4.27 Later stage of cracking on Beam B4.............................................................................82

4.28 Failure mode of Beam B4 .............................................................................................82





5.1 Load-midspan deflection relationship for Beam B1 and Beam B3 ..............................115

5.2 Load-steel strain relationship for Beam B1 and Beam B3 ...........................................115





xii

5.7 Pattern of crack for all beams .......................................................................................118

5.8 Load-crack width relationship for all beams ................................................................119

5.9 Load-concrete strain for all beams................................................................................119

5.10 Failure mode for all beams ...........................................................................................120

5.11 Load-midspan deflection at service load for beams tested under static conditions......121

5.12 Load-crack width at service load for beams tested under static condition ...................121

5.13 Stress-strain model for concrete ...................................................................................122

5.14 Stress-strain model for compression reinforcement .....................................................122

5.15 Stress-strain models for tension reinforcement ............................................................122

5.16 Moment-curvature, and Moment-steel strain relationship for beams tested under

static conditions ............................................................................................................123

5.17 Deflection calculation ...................................................................................................124

5.18 Theoretical and experimental load-midspan deflection for Beam B1 ..........................125

5.19 Theoretical ad experimental load-midspan deflection for Beam B2 and Beam B3 .....125

5.20 Stress-strain model for modified MMFX steel .............................................................126

5.21 Theoretical and experimental load-deflection for Beam B3.........................................126

5.22 Ultimate steel strain-reinforcement ratio for 4000 psi concrete ...................................127

5.23 Ultimate steel strain-reinforcement ratio for 7000 psi concrete ...................................128

5.24 Ultimate steel strain-reinforcement ratio for 10000 psi concrete .................................129

5.25 Ultimate steel strain-reinforcement ratio for Grade 60 steel model .............................130

5.26 Ultimate steel strain-reinforcement ratio for actual MMFX steel model .....................131

5.27 Ultimate steel strain-reinforcement ratio for modified MMFX steel model ................132

5.28 Normalized nominal moment-reinforcement ratio for 4000 psi concrete ....................133

5.29 Normalized nominal moment-reinforcement ratio for 7000 psi concrete ....................134

5.30 Normalized nominal moment-reinforcement ratio for 10000 psi concrete ..................135

5.31 Normalized ultimate moment-reinforcement ratio for 4000 psi concrete ....................136

5.32 Normalized ultimate moment-reinforcement ratio for 7000 psi concrete ....................137

5.33 Normalized ultimate moment-reinforcement ratio for 10000 psi concrete ..................138

xiii

NOTATIONS

a = distance between a point load and support (in)

A = mAe , effective tension area of concrete surrounding the main tension

reinforcing bars and having the centroid as that reinforcement, divided by

the number of bars (in2)

Ac = area of concrete (in2)

As = area of tension steel reinforcement (in2)

As’ = area of compression steel reinforcement (in2)

c = neutral axis depth taken at the extreme compression fiber (in)

Co = numerical constant of 76x10-6 in2/kip

C = internal forces in compression zone of concrete (kip)

Cc = internal force in compression zone from concrete (kip)

Cs = internal force in compression zone from steel (kip)

dc = thickness of concrete cover measured from the extreme tension fiber to the

center of the bar located closest to that fiber (in)

Ec = elastic modulus of concrete (ksi)

Es = elastic modulus of steel (ksi)

fc = concrete stress in compression (psi)

= compressive strength of concrete calculated from concrete strain at any given

value below εo (ksi)

fct = concrete stress in tension (ksi)

f’c = specified compressive strength, compressive strength of concrete cylinder

at time of testing (ksi)

f″c = concrete stress corresponding to eighty-five percent of the compressive

strength at the time of testing (ksi)

fr = modulus or rupture of concrete (ksi)

fs = steel stress in rebar in tension (ksi)

fy = yield stress in rebar in tension (ksi)

fsu = ultimate stress in rebar in tension (ksi)

xiv

fsf = failure stress in rebar in tension (ksi)

fS.L. = steel stress at serviceability level (ksi)

I = moment of inertia (in4)

Ieff = effective moment of inertia (in4)

Ig = gross uncracked section moment of inertia (in4)

L = length of clear span (in)

m = number of bars

Mn = nominal flexural strength of a section (kip-in)

2' bdfM

c

n = normalized nominal moment

2' bdfM

c

nφ= normalized ultimate moment

P = applied load, load (kip)

T = internal forces in tension zone of concrete (kip)

Tc = internal force in tension zone from concrete (kip)

Ts = internal force in tension zone from steel (kip)

w = crack width in the tension face of the beam

y = a distance measured from the neutral axis to the corresponding force (in)

yt = distance from neutral axis to extreme fiber of concrete in tension (in)

ix = distance from the origin to ix (in)

1+ix = distance from the origin to 1+ix (in)

β = the ratio of the distance to the working stress neutral axis from the extreme

tension fiber and from the centroid of the main tension reinforcement

∆ = deflection (in)

∆S.L. = deflection at serviceability level (in)

ix∆ = change in distance between 1+ix - ix (in)

εs = steel strain in rebar (in/in)

εo = concrete strain at the extreme compression fiber corresponding to the

maximum concrete stress (in/in)

xv

εc = concrete strain at the extreme compression fiber (in/in)

εcu = ultimate concrete strain at the extreme compression fiber (in/in)

εy = yield strain in rebar (in/in)

εsu = ultimate strain in rebar (in/in)

εsf = failure strain in rebar (in/in)

εt = net tensile strain in the extreme tension steel (in/in)

ρ = tension steel reinforcement ratio

ρ’ = compression steel reinforcement ratio

ρb = balanced reinforcement ratio

ρductility = minimum ductility reinforcement ratio corresponding to εs of 0.005 in/in

ρmax = maximum reinforcement ratio corresponding to εs of 0.004 in/in

ρmin = minimum reinforcement ratio corresponding to y

c

ff '3

φ = reduction factor for flexural reinforced concrete member

Φ = curvature at given strain increment (rad/in)

iΦ = curvature corresponding to ix (rad/in)

1+Φ i = curvature at 1+ix (rad/in)

1

CHAPTER 1

INTRODUCTION

1.1 GENERAL

Corrosion in conventional steel rebar leads to numerous problems arising from design

life reduction in structural concrete members. Previous solutions to delay corrosion

problems consisted of sensible construction techniques, such as adequate concrete cover

depth, high corrosion-resistant cements, and organic and inorganic coating of conventional

steel. However, these protection types will only prolong the life of concrete structures. The

last alternative to help prevent corrosion problems in reinforced concrete members is to

replace the conventional steel with a highly corrosion resistant material, such as corrosion-

resistant alloys, composites, or clad materials. Although composite materials exhibit

excellent corrosion-resistance, some suffer from low strength properties, excessive deflection

at service load due to a low elastic modulus, difficulties in construction, and high prices.

Recently, a new type of high-corrosion resistant steel, commercially known as

MMFX (Micro-composite Multi-structural Formable Steel), has been developed by MMFX

Technologies Corporation, USA. The producer of MMFX steel claims that the material has a

very high service life along with high strengths, high corrosion resistance, and excellent

mechanical properties. These properties make MMFX rebar an excellent alternative

reinforcement for structural concrete members that are exposed to severe environmental

conditions.

2

Due to the lack of documented resources on the MMFX steel flexural performance as

a flexural reinforcement in concrete members, an investigation on this topic was carried out

by North Carolina State University to provide a better understanding of the MMFX

reinforcing steel to the construction industry and general public. This research focused on

the flexural behavior of rectangular beams reinforced by MMFX rebars.

1.2 OBJECTIVE

The main objective of this research program was to investigate the flexural behavior

of rectangular concrete beams reinforced by MMFX rebars. The flexural performance of the

MMFX reinforcing steel was evaluated in this thesis in terms of flexural cracks, deflections,

strains, and failure modes. This research is the first of its kind to provide design

recommendations on the use of MMFX for concrete structures.

1.3 SCOPE

A total of four 18″x12″x16′ rectangular concrete beams were fabricated and tested to

failure in this experimental program. Three beams were tested under monotonic loading,

while the remaining beam was tested under slow cyclic loading conditions.

All beams were reinforced with two #4 Grade 60 steel rebars in the compression side.

All beams were reinforced against shear failure by placing twenty-seven #4 Grade 60 steel

closed-type stirrups along the length of the beam. The tension reinforcements included #6

Grade 60 steel in one beam and # 6 MMFX steel in the other three beams.

3

A literature review on the flexural behavior of concrete beams reinforced by MMFX

steel is presented in Chapter 2. Civil engineering applications and the material characteristics

conducted by various laboratories along with advantages of MMFX reinforcing steel in

comparison to other reinforcing materials are also provided in Chapter 2.

Chapter 3 presents a detailed description on the experimental program, including the

test specimens, fabrication of the specimens, material properties, instrumentation, and the

testing procedure in static and slow cyclic loading.

Detailed experimental results are given in Chapter 4. The experimental results

include the observed behavior at the time of testing, which is presented in various graphical

displays. A summary of the data is presented at the end of this chapter.

Chapter 5 consists of an in depth discussion of the test results, analytical models,

verification of analytical models, parametric study, and design recommendations.

Summary, conclusions, and recommendations for future studies are given in the last

chapter, Chapter 6.

4

CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

Corrosion of steel reinforcement in concrete structures is a classical worldwide

problem leading to the deterioration of Civil Engineering infrastructures. The primary cause

of corrosion related to deterioration consists of chloride-induced corrosion due to salt,

presence of oxygen, aggressive environment due to high temperatures, humidity, and marine

exposures. In addition, shrinkage and flexural cracks allow more intrusion of chloride ions,

which is acid precipitation from the burning of fossil fuel, and carbonic acid from carbon

dioxide in the atmosphere. The combination of these chemicals, along with moisture and

oxygen, eventually penetrate to the level of the steel reinforcement. This process destroys a

passive barrier against corrosion in steel and accelerates the corrosion mechanism. The rate

of steel corrosion also depends on the steel composition, grain structure, and presence of

residual stresses from fabrication. Factors that attribute to steel corrosion also include what is

in the natural surrounding environment, such as oxygen, water, ionic species, pH and

temperature. Once corrosion sets in the reinforcing steel bars, a corrosion product, rust,

exerts substantial force on the surrounding concrete area. This causes delamination, spalling

of the concrete section, and eventual serious deterioration of concrete structures.

The causes of rapid and premature deterioration in concrete bridges and structures,

due to corrosion of conventional steel rebar, has been established and documented since the

1960’s [9]. Significant corrosion in steel reinforcement is accountable for loss of aesthetic

5

value, reduction of structural strength, shortening of the structure service life, and possible

death or injury due to corrosion-induced failure. It has been documented that billions of

dollars are required annually to repair or reconstruct concrete structures whose life cycle was

shortened or eliminated as a result of corrosion [19]. According to the U.S. Department of

Commerce Census Bureau, the dollar impact of corrosion on highway transportation is

considerable. The annual direct cost of corrosion for highway bridges is estimated to range

from 6.43 to 10.15 billion dollars [21]. Life-cycle analysis estimates indirect costs due to

traffic delays and loss of productivity exceeds ten times the cost of corrosion.

Many techniques have been studied to delay the corrosion rate. Engineers and

scientists are continually brainstorming for solutions to these corrosion-induced problems. In

order to provide additional protection against corrosion, adoption of corrosion prevention

measures should be considered, such as, the use of sensible construction designs, adequate

concrete cover depth, low-permeability concrete, corrosion-inhibiting admixtures, and coated

reinforcing steel. However, these types of measures alone will only prolong the life of the

structures, since concrete has tendency to crack and will ultimately result in the corrosion of

steel. Thus, the last line of defense depends on the reinforcing steel itself. In order to

eliminate corrosion problems altogether, engineers and scientists must make the rebar

resistant to corrosion. To achieve this goal, coating of rebar with organics and metallic

coating, corrosion-resistant alloys, composites, or clad materials are being used for concrete

structures.

6

Epoxy coated rebars (ECR) have gained popularity among bridge related applications

since the 1970’s [9]. However, long-term efficiency of ECR has recently come into question

[8]. Corrosion-resistant alloys and clad materials are more expensive and take up more

reinforcing space due to the lower design strength [9]. The use of composite reinforcing

agents, such as fiber reinforced polymers, are undesirable due to their low stiffness and lack

of ductility [14].

Recently, a more promising solution against corrosion emerged. A new type of steel

called Microcomposite Multi-Structural Formable Steel (MMFX) was developed. The

company claims that MMFX steel has high-corrosion resistance, high-strength, and superior

mechanical properties compared to conventional steel. However, the steel’s actual

mechanical properties and behavior as a flexural reinforcement in concrete structure are

relatively unknown and have not been well documented in literature.

The remainder of this chapter will provide information on definitions, current

applications in Civil Engineering, the material properties of MMFX steel, and literature

reviews on previous research works based on the flexural behavior of concrete members

reinforced with MMFX rebar.

2.2 DEFINITION OF MMFX [16]

MMFX was invented by Professor Gareth Thomas. Professor Thomas is currently

the MMFX Vice President of Research and Development and a graduate school professor of

Material Science at the University of California at Berkeley. MMFX, microcomposite steel,

7

was the result of twenty-five million dollars of research in micro and nano technologies

sponsored by the Department of Energy.

The MMFX Corporation claimed that the company used proprietary methods and

processes to control the MMFX’s material properties at the atomic level. The atomic

resolution capability of the modern electron microscope was used to examine, manipulate,

and perform micro structural changes to the mechanical properties of the material. The

result of the “design by first principles” developing process created strong, tough, and

corrosion-resistant steel. MMFX steels were the first products to use micro and nano

technology.

To slow down or eliminate the corrosion rate, microgalvanic cells, a driving force of

formation of Fe(OH)2 Ferrous Oxides or rust, must be minimized. Therefore, by minimizing

or eliminating the formation of carbides in the conventional steel’s microstructure, corrosion

activity can be minimized or even eliminated. By utilizing transmission electron microscopy

(TEM) techniques to modify the conventional steel’s morphology, MMFX steel’s “plywood”

effect lends superior mechanical properties [15]. MMFX steel possess high strength, good

ductility, and better toughness in comparison to conventional steel reinforcements.

2.3 MATERIAL CHARACTERISTICS OF MMFX

In this section, mechanical properties of MMFX steel will be compared to

conventional steel.

8

2.3.1 Corrosion Resistance [16]

An Accelerated Chloride Threshold (ACT) test, shown in Figure 2.1, was carried out

by Texas A&M University in August of 2000 to provide a quantitative measure of the

MMFX steel’s and conventional steel’s corrosion resistance. According to the results, the

MMFX steel has little corrosion tendency in comparison to A615 steel in a highly corrosive

saline solution during a period of 18 days. The findings show that the highly corrosive-

resistant nature of MMFX steel should provide increased structural concrete service life. The

highly corrosive-resistant behavior of MMFX could also lead to the reduction of the concrete

cover depth and therefore increase of flexural capacity in the member. Design life of 75

years prior to corrosion is conservatively claimed by the MMFX Corporation.

2.3.2 Strength Parameter

An experimental program was conducted at North Carolina State University’s

Constructed Facilities Laboratory (CFL) to provide a comprehensive explanation of MMFX

steel rebar’s fundamental material properties [11]. Strength values, which include tension,

compression, and shear strength of the straight MMFX rebars, were tested and compared to

the strength values of A615 Grade 60 steel.

Tensile strength and stress-strain behavior from MMFX and A615 Grade 60 steel

rebars were obtained from tension testing by using a 2-inch gage length, according to the

Standard Tension Test, ASTM A370-02 [7].

9

The results from tension testing, Figure 2.2, shows that Young’s modulus of elasticity

of MMFX steel and A615 Grade 60 steel are the same with a value of 29,000 ksi. The results

show that MMFX rebar stress-strain behavior does not exhibit any yielding plateau.

However, the MMFX steel exhibits a higher 0.2 % offset yield and ultimate strength than the

A615 Grade 60 reinforcing steel. The higher yield strength allows the same steel structure

section to carry higher loads without suffering permanent deformation. On the other hand,

the higher strength could allow material reductions for specific construction applications,

such as highway bridges and high-rise buildings. The reduction of rebar material quantities

can simplify and reduce construction costs during field installation. A similar conclusion

was also made from tensile tests conducted by the University of California - San Diego [16].

Compression test results from the MMFX and A615 rebars indicated that MMFX

steel also has higher yield strength. Similarly, both materials have the same stiffness. For

conventional reinforcing steel rebars, the stress-strain curve in compression is similar to the

one in tension, which exhibits initial elastic portion, a yield plateau, and a strain hardening.

2.3.3 Fatigue [16]

Comparative fatigue tests for MMFX and A615 was performed according to ASTM

E466. The low S-N curves with a fatigue limit of 10,000,000 cycles were conducted by

Dirats Laboratories, Massachusetts [16]. The S-N curve for both types of steel, Figure 2.3,

demonstrates that MMFX steel is approximately 60 percent higher in fatigue resistance when

compared to A615 steel.

10

2.3.4 Toughness [16]

MMFX steel proves to have high-energy absorption (toughness), evident from the

large plastic deformation area in the stress-strain curve. This property is desirable and allows

a structure with MMFX reinforcement to dissipate energy during high impact loading

conditions, such as punctures, penetrations, earthquakes, etc.

2.3.5 Brittleness [16]

Lower steel brittleness allows the reinforcing steel to retain the load carrying

capabilities at a wider range of temperatures, especially in severely cold regions. A

comparative brittle fracture experiment of MMFX and A615 steel took place at Durkee Test

Lab, California. The test was performed according to ASTM E23. Experimental results of

ASTM E23, Figure 2.4, indicate that MMFX steel retains its strength at a temperature that is

approximately 100 degrees colder than conventional steel.

2.4 REINFORCING PRODUCT EVALUATION

In order to determine the reinforcing capabilities of the MMFX rebar, a reinforced

product evaluation must be analyzed and compared with several existing products [16]. The

existing products used for reinforcing applications consist of A615, epoxy coated rebar,

Stainless Steel Clad, 304 SS, and 316 SS. Installation cost and estimated service life, along

with each product’s advantages and disadvantages are presented below. Rebar installation

costs are analyzed based on material price, transportation, fabrication, and cost of

installation. Table 2.1 displays the product evaluation information taken from the MMFX

Product Bulletin.

11

Conventional steel rebar, A615, serves as a point of reference for the alternative

reinforcements presented here. Regular black bar is common and the most inexpensive, thus

making it the most popular material for reinforced concrete. However, a conventional rebar

provides the least amount of corrosion-resistance, which could lead to a concrete structure

life cycle of 15 to 30 years.

Epoxy coated rebar was introduced during the 1970’s. For a period of time, Epoxy

coated rebar posted a promising alternative against corrosion [17]. Until 1986, after 6 years

of construction, Florida DOT reported that the Long Key Bridge showed signs of corrosion.

Many investigations on the long-term performance of the ECR indicated mixed results,

ranging from poor to satisfactory performance. Corrosion performance depends heavily on

the field fabrication of epoxy coating, because the coating needs to be placed on the A615

rebar after fabrication, but prior to shipment for installation [9]. Coating damage, such as

nicks, scratches, or holidays, often initiate localized corrosion. In 18 Virginia highway

bridge decks, debonding of properly coated rebar due to the loss of adhesion occurred in as

little as 4 years (from properly constructed concrete bridge) after placement [17]. The epoxy

coated rebar has an estimated service life of 20 to 40 years, due to the mixed results in

surface imperfection and lack of coating thickness control. Field cutting, installing,

inspecting and transporting of ECR can lead to a 50 percent increase in material cost when

compared to the A615 conventional rebar cost. Knockdown design factors must be applied

to take into account the amount of loss due to the shear/bond induced by the coating material.

12

Stainless steel differs mainly from the carbon steel composition, structure, and

properties. Conventional steel is considered to be “Stainless” when the chromium content is

greater than 12 percent. There are three types of stainless steels available, ferritic, austenitic,

and martensitic. Austenitic stainless steel grades 304 and 316 are the most popular stainless

steel used for reinforcement. Stainless steel achieves its superior corrosion resistance and 75

years or greater design life thanks to a more stable form of thin passive chromium oxide film.

In recent years, stainless steel has gained some popularity and replaced carbon steel in areas

where carbon steel rebar is judged to be at a high risk of corrosion [9]. Stainless steels are

very expensive and generally have lower yield strengths than carbon steels, thus resulting in

high material cost and requiring additional reinforcing rebar. The standard rebar length of 40

feet is not yet available, therefore, permitting the stainless steel to be used in a long highway

bridge over-pass.

Stainless steel cladding provides similar corrosion-resistance to that of the solid

stainless bar. This material can be mechanically handled in the same way as the black bar.

However, field cutting, handling and inspecting must be performed, which leads to increased

installation and coating damage repair costs. These problems increase the installation cost to

around 200 percent in comparison to A615 Grade 60 steel. In some cases, the bending of

smaller sized bars creates splitting and cracking, or debonding, of cladding. This leads to

corrosion in the substrate material, A615. Similar to solid stainless steel, a lack of standard

40-foot rebar also requires additional field splicing.

13

Compared to other reinforcing agents, MMFX rebar has excellent corrosion-

resistance, which is similar to solid stainless steel and stainless steel cladding materials.

MMFX’s technologies allow high design yield strength, which substantially reduces rebar

quantities and simplifies installation costs. Standard fabrication techniques are applicable at

both the steel fabricators, and in the field. In addition, MMFX rebar has advantages in that it

does not suffer from coating damage or corrosion due to surface imperfections, nor does it

require field installation or extra care during the shipping process. It is possible that by

switching from A615 Grade 60 rebar to MMFX rebar would cause a slight increase in

material cost. However, it could be more economical if used effectively.

2.5 FIELD APPLICATIONS [16]

Current Civil Engineering applications, shown in Figure 2.5 that use MMFX rebars

are gaining popularity. MMFX rebar has been integrated in commercial, residential, and

transportation projects. In commercial building, MMFX microcomposite steel rebar has been

used as tension bracing at the Colorado Commercial Building Skylight in Longmont,

Colorado. On residential projects, MMFX rebar has been used as a substitute to conventional

steel for residential house slabs in a highly corrosive coastal area of Florida. In three

government highway bridge projects, MMFX rebars were incorporated into new bridge decks

as reinforcement for the Iowa Department of Transportation (DOT) project, replaced bridge

deck reinforcement for Kentucky DOT Bridge, and used as shear reinforcement for bridge

girders in the Oklahoma DOT construction project.

14

2.6 FLEXURAL BEHAVIOR OF CONCRETE BEAMS REINFORCED BY MMFX

REBAR

Ashley et al. (2002) provided the first report on the structural performance of MMFX

reinforcement [2]. As requested by the Florida Department of Transportation, a series of 4

beam tests were conducted to observe the reinforcing behavior of MMFX. The results were

compared to the behavior of A615 Grade 60 reinforcing steel.

The beam dimensions were 12 inches deep, 12 inches wide, and 16 feet long with a

clear span of 14 feet. Beam B1 was constructed to observe a pure bending behavior of

MMFX reinforcing bar. Beam 2 and Beam 3 were tested to investigate the bond and

development of MMFX steel. Two #6 MMFX rebars were used as tension reinforcement for

Beam 1, Beam 2, and Beam 3. The bottom reinforcement of Beam 4 consisted of three #10

MMFX rebars in order to observe shear behavior. The flexural result of Beam B1, shown in

Figure 2.6, indicated that similar values of section stiffness, cracking load, and section

stiffness after the first crack were comparable to a controlled beam. The load-deflection

behavior of the two beams is fairly similar up to the yield loading of Grade 60 steel. The

MMFX beam has about 1.80 times the flexural strength and 40 percent more ductility than

the Grade 60 beam. The Grade 60 beam experienced 22 percent more midspan deflection

than the MMFX beam. The researcher concluded that the flexural performance of the

MMFX reinforced beam compares favorably to the conventional Grade 60 steel, and the

difference in beam behaviors is due to the fundamental difference in the material properties

of each material. Moreover, due to the lack of a defined yield point and its high strength

property, engineers must pay attention in the design of the MMFX reinforced beam.

15

At University of North Florida, Malhas (2002), published the report “Preliminary

Experimental Investigation of the Flexural Behavior of Reinforced Concrete Beams Using

MMFX Steel” [13]. The two primary objectives of this program was to study the flexural

behavior of concrete beams reinforced with MMFX steel and to correlate the ACI provisions

with the experimental results. In this report, 22 beams with dimensions of 12 inches wide, 18

inches high, and 13 feet long were fabricated for this program. Two classes of 6200 psi

(series A), and 8700 psi (series B) concrete were used. Three different reinforcement ratios

based on the ACI maximum reinforcement ratio were used in the design process: 0.25ρmax,

0.5ρmax, and 1.0ρmax. Grade 60 steel was also used as a control specimen in two of the beams

for each of the concrete strengths (Series C). The purpose of the two beams reinforced with

the Grade 60 steel was to establish an experimental benchmark for the MMFX beams.

Beams in series A, and B were all reinforced with MMFX steel. All beams were tested under

a four-point loading configuration. Each specimen was monotonically loaded to failure. The

experiment showed that all of the MMFX reinforcing beams failed in a ductile manner with a

level of ductility comparable to that of Grade 60 steel [13]. The failure mode was classified

as ductile flexural failure with significant straining preceding the crushing of concrete. The

MMFX steel performed well in both low and high-strength concrete and with no premature

failure. All cracks were primary controlled by the spacing of the stirrups. All beams

functioned in a satisfactory manner and without shear or bond failure. MMFX beams with

smaller amounts of reinforcement experienced more severe failures. All concrete crushing

occurred in the pure bending region. The monitored deflection of the MMFX beam at the

service load should satisfy the permissible value. The conclusion was made that the MMFX

reinforcing beams were comparable in behavior to the Grade 60 Beams, except there was a

16

more pronounced stiffness reduction after the initiation of cracking. Based on the findings,

the direct substitution of conventional steel with MMFX steel seems reasonable. The

bending moment was predicted accurately using the ACI method. Evaluation of the flexural

behavior of all 22 beams based on moment-curvature relationship, load-deformation, ultimate

strength, ultimate curvature, beam stiffness, crack formation, crack width, and deflection

under service load confirmed the consistency and reliability of the MMFX steel in concrete

applications.

Galloway and Chajes (2002) also completed the “Application of High-Performance

Materials to Bridges,” with sections on “Strength Evaluation of MMFX Steel.” In this

report, four MMFX, two Grade 60, and one stainless Steel clad beams were designed, cast,

and tested in the three point bending configuration. Three MMFX beams were reinforced

with 1 #4 rebar and one with 1 #6 rebar. One Grade 60 and steel clad beam was reinforced

with 1 #6 rebar. The remaining beam was a Grade 60 beam with 1 #4 reinforcement. Three

beams reinforced with #4 bars were fabricated to illustrate the high strength capabilities of

the MMFX steel. The concrete at the time of testing was equal to 4000 psi. All seven beams

were measured at 4 inches wide, 6 inches long and 5 feet long. The measured yield load of

the MMFX demonstrates that the MMFX is stronger than A615 steel in both tension and

flexure. The observed failure mode was the crushing of concrete before the steel yielded.

Galloway and Chajes (2002) did not recommend a direct substitution of MMFX steel for

A615 Grade 60 rebar, due to brittle failure of the over reinforced beams. Galloway also

indicates that after the MMFX beam reached its yielding, the beam continued to sustain part

17

of the applied load. The researcher stated that the MMFX reinforced beam behaved this way

because of the nonlinear relationship of the MMFX material [12].

In July 2002, the College of Engineering and Mineral Resource of West Virginia

University submitted a comprehensive report on “Bending Behavior of Concrete Beams

Reinforced with MMFX Steel Bars” to the MMFX Corporation. Vijay et al. (2002)

investigated the bending behavior of concrete beams reinforced with MMFX steel bars. Four

concrete specimens, with dimensions of 12 inches wide, 18 inches deep, and a clear span of

13 feet long, were reinforced with different sized MMFX rebars. Each specimen was loaded

in at least 3 cycles by increasing the applied load in each cycle until the specimen reached

failure. The principle variable parameter was the percentage of reinforcement and concrete

type. The percentage of reinforcement varied from 0.079 percent to 0.19 percent. Two

compressive strengths of concrete were used: 8170 psi (Beam B1, Beam B3), and 11190 psi

(Beam B2, Beam B4).

The researcher reported that the stress-strain behavior of the MMFX rebars could be

accurately represented, up to 5 percent strain, using the following exponential models

expressed in Equation 2.1.

)1(068.164 05.182 sef sε−−= for #4 rebars

)1(173 168 sef sε−−= for # 8 rebars Eqn. 2.1

where,

fs = steel stress in the MMFX rebar

εs = steel strain

18

The maximum moment was predicted accurately based on current concrete theories

and by using the iterative process [20]. The ratio of experimental moment to theoretical

moment ranges from 0.87 to 1.04. Deflection at midspan was calculated based on the

effective moment of inertia provided by ACI 318-99 and modified moment of inertia for

four-point bending [20]. All deflection predictions were calculated based on four-bending

tests, described by Equation 2.2, while using a constant modulus of elasticity with adjusted

multipliers, constant modulus of elasticity with modified moment of inertia, and a varying

modulus of elasticity approach. The predicted results from the first and second method did

not provide a good representation of the MMFX rebar load-deflection behavior. The third

approach provides good correlations between the experimental deflection and theoretical

deflection for a stress range of up to 75 ksi in the #8 bars. Crack calculation based on

Gergely-Lutz’s expression for crack width, described in Equation 2.3, gave reasonable

results, but needed further improvement for better accuracy. All beams satisfy the crack limit

of 0.016 inch and a deflection of 360L at a stress level below 40 ksi; however, the crack width

and deflection criteria remain in question at the above stress level. All beams exhibited

significant straining in steel prior to crushing failure.

−=∆ 3

3343

24 La

La

IEPL

c

Eqn. 2.2

where,

∆= deflection

P = service load

19

Ec = elastic modulus of concrete

I = effective moment of inertia

a = distance between a point load and support

L= clear span length

3 AdfCw csoβ= Eqn. 2.3

where,

w = crack width in the tension face of the beam

β = the ratio of the distance to the working stress neutral axis from the

extreme tension fiber and from the centroid of the main tension reinforcement

fs = service load stress in the steel

dc = thickness of concrete cover measured from the extreme tension fiber to

the center of the bar located closest to that fiber

A = mAe , effective tension area of concretes surrounding the main tension

reinforcing bars and having the centroid as that reinforcement, divided by the

number of bars

m = number of bars; for different sizes use AbAsm =

Co = constant of 76x 10-6 in2/kip

The cracking moment was predicated accurately for all previous studies. The

classical equation, equation 2.4, was used to predict the cracking moment.

20

t

grcr y

IfM = Eqn. 2.4

where,

fr = modulus rupture of concrete

Ig = moment of inertia of gross uncracked section about the centroidal axis,

neglecting reinforcement

yt = distance from neutral axis to extreme fiber of concrete in tension

21

Table 2.1: Product Evaluation Table [16] Rebar Product Approximate Ratio of Adjusted Ratio of Estimated Years Classification Installed Cost of Rebar Installed Cost for of Service Life

to A615 Rebar Design Yield Strength (Years)

A615 1 1 15 - 30 Epoxy Coated (A615) 1.4 - 1.6 1.4 - 1.6 20 - 40

Stainless Steel Clad (A615) 2.1 - 2.4 2.1 - 2.4 75 + 304 SS 4.3 - 4.5 5.2 - 5.9 76 + 316 SS 4.7 - 4.9 5.7 - 5.9 77 + MMFX 2 1.5 - 1.7 1.1 - 1.3 78 +

22

Figure 2.1: Accelerated Chloride Threshold (ACT) test on MMFX steel [16]

Figure 2.2: Typical stress-strain curve of MMFX, and Grade 60 steel in tension [11]

.M * •• •• ; .

• !M • • •

• 0

0 OM

--

M"'FXSTU~ "_1,,,_ '''''' ."

...... M.~_.

O. " ... Str .... 'lnIlnj

... ...

23

Figure 2.3: Typical fatigue limit of MMFX, and Grade 60 steel [16]

Figure 2.4: Typical Brittle Fracture Data of MMFX, and Grade 60 steel [16]

24

Figure 2.5: Field application of MMFX steel [16]

Figure 2.6: Load-deflection behavior by Marcus H. Ansley [2]

25

CHAPTER 3

EXPERIMENTAL PROGRAM

3.1 GENERAL

The main objective of this experimental program is to investigate the flexural

behaviors of MMFX steel as reinforcement for concrete structures. In addition, the research

program is the first of its kind to provide design recommendations on the use of MMFX for

concrete structures. An additional beam using A615 Grade 60 steel was cast and used as a

control specimen. A total of four large-scale rectangular concrete beams were tested under a

four-point flexure loading condition. Two beams reinforced with MMFX bar had the same

reinforcement ratio as the beam reinforced with Grade 60 steel. Three beams were tested

under monotonic loading, while the other was tested in a slow cyclic condition. The third

beam reinforced with the MMFX bar had a lower reinforcement ratio to utilize the high

strength properties. The third beam was tested under the monotonic condition. All beams

tested in this program had the same size of longitudinal rebar.

The main parameters included the reinforcement ratio and type of loading. The

overall performance of the tested specimens was evaluated based on the overall flexural

behavior. The different limit states used to evaluate flexural performance were:

a) Flexural cracking load

b) Crack pattern and crack width

c) Deflection under load

d) Ultimate flexural strength

e) Failure mode

26

3.2 TEST SPECIMENS

In this section, design of the specimens, flexural reinforcement, and shear

reinforcement are discussed.

3.2.1 Design of the Specimens

All specimens were designed to have a large-scale dimension to simulate typical field

behavior of concrete beam applications. The selected dimensions were 12 inches wide, 18

inches high and 16 feet long. All beams were designed to achieve the minimum strain in the

steel of 0.005 in/in. The reinforcement ratios for all beams satisfied the minimum and

maximum value recommended by ACI 318-02 [1]. All beams were designed using a

nominal compressive strength of concrete of 5000 psi. Specimens were marked B1, B2, B3,

and B4. Types of loading consisted of static loading for three specimens (Beam B1, B2, and

B3) and cyclic loading on the remaining specimen (Beam B4). All specimens were loaded

up to failure using a four point flexural test.

Beams B1, B2, B3, and B4 had reinforcement ratios of 0.00704, 0.00469, 0.00704,

and 0.00704 respectively. Beam B1 was the only beam reinforced with Grade 60 bars on the

tension side with a reinforcement ratio of 0.00704. Beam B1 was used as the control

specimen for the MMFX beams. Beam B3 was designed to have the same reinforcement

ratio as beam B1. An equal amount of reinforcement was selected to observe the flexural

behaviors of the MMFX in comparison to the beam reinforced with Grade 60. Beam B2 was

designed to have a lower reinforcement ratio than beam B3 of 0.00469 in order to utilize the

high strength properties of MMFX steel. Beam B4 was constructed to observe and evaluate

27

the flexural performance under the slow cyclic loading condition. All beams were designed

to comply with a new ACI code of minimum ductility (εs= 0.005 in/in). Table 3.1

summarizes the test matrix.

3.2.2 Flexural Reinforcement

All beams were reinforced in both tension and compression as summarized in Table

3.1. Two types of longitudinal steel were used as flexural reinforcement, A615 Grade 60,

and MMFX high strength steel.

Three #6 Grade 60 longitudinal rebars were used as bottom reinforcement for Beam

B1. Three #6 MMFX longitudinal rebars were used as the bottom reinforcement for Beam

B3, and Beam B4. Beam B2 was reinforced with two #6 MMFX steel rebars.

Two #4 Grade 60 longitudinal rebars were used for compression reinforcement for all

beams to simplify the construction of the steel cage. Figure 3.1 illustrates the typical

reinforcement for B1, B3, and B4.

3.2.3 Shear Reinforcement

To prevent an undesired shear failure in the beams, shear reinforcement was

provided. All beams had an identical stirrup, as shown in Figure 3.2.

A total of 20 closed type Grade 60 #4 stirrups were positioned at 8 inch spacing

within the constant shear regions. Two additional stirrups with 3 inch spacing were placed at

28

the anchorage to prevent a possible slippage failure. Buckling of the compression

reinforcement at the ultimate load was avoided by placing another 3 stirrups at 9 inch spacing

within the zero shear regions, therefore, a total of 27 stirrups were used per beam. A typical

of shear reinforcement along the beam is shown in Figure 3.3.

3.3 MATERIAL PROPERTIES

In this section, concrete and steel mechanical properties are reported based on test

results conducted in accordance with ASTM standards.

3.3.1 Concrete

Two batches of normal Portland cement concrete were used in this program. Beam

B1 and B2 were the first batch, while Beams B3 and B4 were the second batch. The concrete

was delivered by the local ready-mix concrete supplier.

The cement mix proportion for the first batch of concrete was 1:1.81:2.88

(cement:sand:aggregate) and had a water to cement ratio of 0.17. The target slump was equal

to 4 inches. The second batch of cement mix proportion was 1:1.79:2.88

(cement:sand:aggregate), and had a water to cement ratio of 0.167. Seven gallons of water

were added to the second batch of concrete to increase the workability and decrease the

slump from 2 inches to an ideal 4.5 inches of slump. About 23 percent of fly ash by volume

of cement was used to enhance the overall strength in both batches of concrete. The strength

estimation based on the water to cement ratio indicated that the actual compressive strength

of the concrete at 28 days should be higher than the 5000 psi targeted strength.

29

In order to determine the actual properties of both batches of concrete, eight 4˝x8˝

inch concrete cylinders were prepared and cured at room temperature. Six compressive tests

and two splitting tensile tests were performed.

Two concrete cylinders were tested at 28 days and two additional cylinders at the

time of testing. This according to ASTM C39-01: Standard Test Method for Compressive

Strength of Cylindrical Concrete Specimens [5]. Two out of the six cylinders from the

compression tests were instrumented with PI-Gages, as shown in Figure 3.4, to determine the

actual stress strain curve of each batch of concrete. The universal testing machine

continuously applied a compressive load to the concrete cylinder.

The loading was applied at a constant rate of 0.05 inches per minute. The maximum

load carried by each specimen was obtained from the screen and recorded. All cylinders

were loaded to failure. The type of failure associated with each specimen in compression

was columnar, as shown in Figure 3.5.

The recorded maximum load was used to calculate the maximum compressive

strength. Compressive strengths associated with the two batches of concrete beams are

presented in Chapter 4.

The remaining two concrete cylinders were tested at the time of testing of each beam,

according to ASTM C496-96: Standard Test Method for Splitting Tensile Strength of

Cylindrical concrete [6]. The load was continuously applied. The loading was monitored at

30

a constant rate within the range of 100 to 200 psi per minute to failure. Similarly, the

maximum applied load indicated by the testing machine was record for each cylinder.

The failure mode was found by subjecting the concrete cylinders to a splitting tension

test. They both were split in half at the vertical axis of the cylinder, as illustrated in Figure

3.6.

The actual stress and strain curves obtained from these auxiliary tests are presented in the

next chapter.

3.3.2 Steel

Tension tests were performed according to ASTM A370-02 to determine the stress-

strain characteristic of the tension and compression reinforcements [3]. The coupon test was

conducted, as seen in Figure 3.7, over 2 inch gages in accordance with ASTM E8-01 [7].

The rebars were cut at 20 and 21 inches in total length for #4 and #6 rebars respectively.

The interested variables will be discussed in terms of modulus of elasticity (Es), yield

strain and strength (εy, fy), ultimate strain and strength (εsu, fsu), and strain and strength at

failure (εsf, fsf). Addition information, such as the proportional limit stress and strain at the

maximum allowable stress of 80 ksi on MMFX, will also be reported. Strength at strain

hardening will be given for #4 and #6 Grade 60 steel rebars. The actual stress-strain curves

for all reinforcements can be found in the next chapter. All tensile properties are reported in

terms of average value in Chapter 4.

31

The failure mode of the reinforcements was found by subjecting them to a tension test

until rupture. This preceded the necking phenomenon, as illustrated in Figure 3.8.

3.4 FABRICATION OF THE SPECIMENS

All specimens were fabricated at the Construction Facility Laboratory of North

Carolina State University.

A formwork was constructed from ¾" thick plywood to have two cells (or two bays)

in order to house two beams at a time. At the same time, each reinforcing steel cage was

carefully assembled to the specifications required. One and a half inch steel chairs were

installed at the bottom of the steel cages to ensure a target of 1-1/2 inch concrete cover. The

form was then sprayed with an oil-based material to simplify removal efforts. The steel

cages were then placed in the form and a series of bracing was installed at the top of the

form. The bracings were located at 4 feet spacing to ensure proper dimensions of the beam,

as shown in Figure 3.9. The form was moved to the pouring site to allow easy access to the

ready mix truck.

Concrete was supplied by a local ready-mix concrete company. Slump tests were

performed within 2.5 minutes after obtaining the sample as stated in ASTM C143-00 [4].

This process was crucial for determining the workability of the concrete. The results of the

slump tests were equal to 4 inches for the first and 4.5 inches for the second batch.

32

The casting of the specimens began when the shoot of the ready mix truck was

lowered to directly pour the concrete into the form. The finishing process followed shortly

thereafter. At the same time, eight 4˝x8˝ cylinders were prepared to determine the strength

parameters. Figure 3.10 illustrates the casting process of the concrete specimen.

Finally, a plastic sheet was placed on top of the concrete specimens as seen in Figure

3.11. The beams and cylinders were left to cure in the same condition for 28 days. The

beams were stripped after 28 days and prepared for testing.

3.5 INSTRUMENTATION

All beams were fully instrumented to measure the applied loads on the beams,

deflections associated with each loading, and strains in concrete and steel, as illustrated in

Figure 3.12.

A total of two electrical resistance strain gages were installed at the location of the

maximum stress on each one of the bottom steel reinforcements to measure strain in the

tension steel. This location was calculated to be at the midspan of the reinforcing agent.

A total of five PI-Gages were installed at critical locations along the top and the side

of the each specimen to measure the strain in the concrete during the loading. Two PI-Gages

were placed on the top of the beam at mid span, while the others three PI-Gages were placed

on the side of the beam at midspan. One PI-gage was at the mid height of the beam, one was

at the level of the top rebars at 2.375 inch from top, and one was at the level of the bottom

33

rebars at 2.375 inch from the bottom. All PI-Gages were bolted onto the surface of the

specimen with epoxy-based material.

Six Linear Variable Differential Transducers (LVDTs) were installed at critical

locations along the top and bottom of each specimen. Two LVDTs were placed side by side

at the bottom of midspan to measure the maximum deflection. Another two LVDTs were

installed on top of each support to measure deflection. Deflections at the locations of the

supports were measured in order to determine the net maximum deflection. The remaining

two LVDTs were placed at the bottom of each concentrate load.

All strain gages, PI-gages, and LVDTs were connected to a circuit board of the data

acquisition system and readings were collected during the time of loading every one second.

Table 3.2 gives the precise location and function of each device.

3.6 TESTING PROCEDURE

3.6.1 Test Setup

After a 28 day curing period, all beams were moved to perform a four point flexural

test. Each beam was tested to failure by the 440 kips-capacity MTS actuator.

A tested specimen was placed on two steel members. The setup was positioned on

top of the strong structural concrete floor, as seen in Figure 3.12. A steel pin support was

carefully seat between the specimen and the steel member at a distance of 6 inches from the

left end of the beam, while a steel roller support was positioned at the same distance but at

34

the right end of the beam. The setup was carefully leveled and aligned to prevent any source

of errors due to the lateral eccentricity.

A W8x12 steel member was selected and attached to the MTS actuator by a high

strength steel bolt as a loading member. The steel member along with the MTS actuator was

then lowered onto the 2 inch wide, 12 inch long, and 6 inch high rigid steel loading plate,

which was attached to the compression side of the beam in order to simulate two-point

loading. The loading plates were installed on the top of the concrete beam at 6 feet from

each support and 3 feet apart. The 12 inch long plates were placed on the top of the neoprene

pad to ensure an even distribution of the concentrated load. The neoprene pad had the same

dimensions of the steel plate.

3.6.2 Preparation for Testing

After the specimen was properly positioned, strain gages, PI-gages, and LVDTs wires

were connected to the data acquisition system. PI-gages and LVDT’s were manually

checked to verify the operational condition. The quick-set plaster was applied between the

loading steel plate and the concrete surface to provide proper contact. The data acquisition

system was thoroughly checked. Figure 3.13 illustrates beam B1 prior to loading.

3.6.3 Testing

Beams B1, B2, and B3 were monotonically tested to failure by the 440 Kips-Capacity

MTS closed loop system machine. The three specimens were subjected to a four-point static

loading under the deflection control mechanism (stroke control) at a typical rate of 0.042

35

inches per minute. The last beam, Beam B4, was loaded to failure under a slow cyclic

configuration at the rate of 0.042 inches per minute. The loading consisted of three load-

unload cycles at 0 to 25 kips, 0 to 42 kips, 0 to 55 kips, 0 to 65.7 kips, 0 to 72.6 kips, and

72.6 to 77.6 kips. The load-unload cycles were determined based on a deflection (∆=0.55

inch) corresponding to applied load at the 80-ksi stress level in the MMFX rebars on Beam

B3. Table 3.3 shows slow cyclic loading configurations on Beam B4.

At the time of testing, load, strain, and deflection information was displayed on the

screen of the data acquisition system and was carefully monitored. Crack propagation and

crack width were visually observed and measured via crack comparator during the tests.

36

Table 3.1: Experimental test matrix

Beam Dimension Bottom ρ ρ min Top ρ' f'c Type of Loading

WxHxL (ft) Reinforcement Reinforcement (psi) B1 1x1.5x16 3 # 6 Grade 60 0.00704 0.00353 2 # 4 Grade 60 0.00213 5000 Static B2 1x1.5x16 2 # 6 MMFX 0.00469 0.00265 2 # 4 Grade 60 0.00213 5000 Static B3 1x1.5x16 3 # 6 MMFX 0.00704 0.00265 2 # 4 Grade 60 0.00213 5000 Static B4 1x1.5x16 3 # 6 MMFX 0.00704 0.00265 2 # 4 Grade 60 0.00213 5000 Slow Cyclic

Table 3.2: Summary of location, and function of each device

Device Location Function

PI-Gage 1 Top-Front of the specimen Measure concrete strain PI-Gage 2 Top-back of the specimen Measure concrete strain PI-Gage 3 At the level of compression steel Measure concrete strain PI-Gage 4 At the middle of the beam Measure concrete strain PI-Gage 5 At the level of tension steel Measure concrete/steel strain

LVDT 1 At Left support Measure deflection LVDT 2 At left loading point Measure deflection LVDT 3 At the bottom-front of the specimen Measure deflection LVDT 4 At the bottom-back of the specimen Measure deflection LVDT 5 At right loading point Measure deflection LVDT 6 At right support Measure deflection

Strain Gage Bottom rebar No. 1 Measure steel strain Strain Gage Bottom rebar No. 2 Measure steel strain

Table 3.3: Testing program of Beam B4

Experimental Deflection (in)Corresponding

Load (kip) Load & Unload

Cycle

0.5∆ 25 3 1 ∆ = 0.55 inch at fs = 80 ksi 42.1 3

1.5 ∆ 55.8 3 2 ∆ 65.7 3

2.5 ∆ 72.6 3 3 ∆ 77.6 3

37

Figure 3.1: Typical reinforcement of Beam B1, B3, and B4

#4 StirrupGrade 60 ksiA total of 27 Stirrups per beam

All the radii are 1.125 "

Stirrup Details

15"

D=2.25"

3.625"

9"

1.12

5"1.

125"

Figure 3.2: Stirrup details for all beams

38

Figure 3.3: Typical distribution of shear reinforcement

39

Figure 3.4: Setup for concrete compression strength test

Figure 3.5: Type of compression failure on the tested cylinder

Figure 3.6: Type of tensile failure on the tested cylinder

40

Figure 3.7: Test setup for tension test

Figure 3.8: Type of tension failure on the tested rebar

41

Figure 3.9: Steel cage and form

Figure 3.10: Casting and finishing of the specimen

Figure 3.11: Curing of the beams

42

Figure 3.12: Test setup and instrumentation

43

Figure 3.13: Typical beam setup

44

CHAPTER 4

EXPERIMENTAL RESULTS

4.1 GENERAL

This chapter presents the experimental results of concrete beams tested to determine

the flexural behavior and the material properties of concrete beams reinforced by MMFX

rebar. Material properties included the measure of concrete strength, and the mechanical

properties of A615 Grade 60 and MMFX steel. Characteristics of the concrete included

compressive and tensile strengths determined at the time of testing of the beams. Mechanical

properties of reinforcing materials included elastic modulus, yield strength, and the ultimate

strength. Experimental results of the four beams included the cracking load, crack pattern,

crack width, deflection, ultimate flexural strength, and failure modes.

4.2 MATERIAL PROPERTIES

In this section, concrete and steel mechanical properties are reported based on test

results conducted according to ASTM standards.

4.2.1 Concrete

4.2.1.1 Compressive Strength

Six concrete cylinders were tested based on ASTM C39-01: Standard Test Method

for Compressive Strength of Cylindrical Concrete Specimens [5]. The compressive strengths

of each set of concrete beam are presented in Table 3.1. The first batch of concrete was used

for Beam B1 and B2, while the second batch was used for Beam B3 and B4.

45

According to Table 3.1, the first set of specimens (Beam B1, and Beam B2) had an

average compressive strength of 7047 psi and a standard deviation of 129.8 psi, while the

second set of specimens (Beam B3, and Beam B4) had an average strength and standard

deviation of 7244 psi and 330.8 respectively. The standard deviation was less than 500 psi as

specified by ASTM C39-01; therefore this confirmed the structural integrity of both batches

of concrete [1]. The average compressive strength of the concrete used was 41 percent

higher than the original design nominal strength.

The actual stress-strain relationship obtained from one compressive cylinder test is

shown in Figure 4.1. The stress-strain behavior of the concrete lacks the descending portion

due to the nature of the applied load control option used by the testing machine.

4.2.1.2 Tensile Strength

Two concrete cylinders were tested according to ASTM C496-96: Standard Test

Method for Splitting Tensile Strength of Cylindrical concrete [7].

The average tensile strength of the first set of concrete, as reported on Table 4.2, is

588.5 psi, which is 11 percent higher than the average tensile strength of second set. A

standard deviation of less than 10 psi confirms a low deviation from the mean.

46

4.2.2 Steel

The results of the tension tests for the reinforcements are presented in Table 4.3. All

tests were conducted in accordance to ASTM E8-01 [7], and ASTM A370-02 [3]. The

properties of each type of steel rebar are discussed in terms of modulus of elasticity (Es),

yield strain and strength (εy, fy), ultimate strain and strength (εsu, fsu), and strain and strength

at failure (εsf, fsf). The reported data is computed as a weighted average determined by the

number of tension tests. The tensile strength of the reinforcements used as flexural

reinforcement is presented in Figure 4.2 and Figure 4.3 for the Grade 60 and MMFX steel,

respectively.

4.2.2.1 Compression and Shear Reinforcements

All beams were reinforced with two #6 A615 Grade 60 steel rebars. The average

yield stress and strain, the average ultimate stress, ultimate strain, average failure stress and

failure strength and corresponding failure strain values were 62.67 ksi, 0.00243 in/in, 93.46

ksi, 0.1223 in/in, 88.19 ksi, and 0.167 in/in respectively. The measured elastic modulus was

about 26000 ksi. The measured yield strength was 2.67 ksi higher than the typical yield

stress of 60 ksi specified by the manufacturer.

4.2.2.2 Tension Reinforcements

Two types of tension reinforcements were used in this experimental program: 1)

A615 Grade 60 steel #6 rebars for Beam B1, and 2) MMFX steel #6 rebars for Beam B2, B3,

and B4.

47

Grade 60 Steel

The measured yield stress of the Grade 60 #6 tension steel was 63.54 ksi. The

average ultimate stress, ultimate strain, failure stress and failure strain were 96.44ksi, 0.1315

in/in, 91.62 ksi, and 0.1617 in/in, respectively. The strain hardening occurred at 63.9 ksi and

the corresponding strain was 0.0117 in/in. The elastic modulus of 27272 ksi was measured at

yield strain of 0.00233 in/in.

MMFX Steel

Two sets of #6 MMFX rebars were used in this experiment. The first set was used to

reinforce Beam B2, while the second set was used to reinforce Beam B3 and Beam B4. The

results from tension tests show similar strength values. The presented results were taken

from the first set of MMFX rebar.

As illustrated in Figure 4.3, the stress-strain behavior of the MMFX steel does not

exhibit any yielding plateau; therefore the yield strength was measured at a specified offset of

0.2% (0.002 in/in) strain. The average offset yield strength for the first set of MMFX rebars

was determined at 123.88 ksi. The ultimate strength, ultimate strain, failure stress and strain

were 178.28 ksi, 0.0534 in/in, 126.32 ksi, and 0.196 in/in respectively. The average

proportional limit for MMFX steel was 84.44 ksi. The Young’s modulus of elasticity of the

MMMF steel was 27510 ksi, which was comparable to that of the conventional steel. The

maximum yielding stress limit specified by ACI for deformed reinforcing rebar was 80 ksi,

which corresponded to an average strain of 0.00314 in/in for the MMFX steel. The

mechanical properties of the second set are given in Table 4.3.

48

In comparison to the ultimate stress specified by the MMFX Corporation of America,

the measured ultimate strength determined at the time of testing was slightly higher by

approximately 3 ksi. The original stress-strain equation of the MMFX steel, displayed in

Equation 2.1, was modified by the trial and error method to compensate for the additional

strength. The new equation is expressed in Equation 4.1.

)1(177 185 sef sε−−= Eqn. 4.1

where:

fs = steel stress of MMFX rebar

εs = steel strain of MMFX rebar

4.3 BEHAVIHOR OF BEAM B1

Beam B1 was the first beam tested under the static loading condition. The top and

bottom reinforcements of Beam B1 were both A615 Grade 60 steel. This beam had a tension

reinforcement ratio of 0.704 percent. The tension reinforcement consisted of three # 6 Grade

60 steel bars. The observed behaviors and experimental results of Beam B1 are reported in

this section.

4.3.1 Flexural Behavior

Initiation of the first crack occurred at a load level of 8.5 kips. Two flexural cracks

occurred in the constant moment region. At around 10 kips, four additional flexural cracks

initiated in the same region and propagated upward. As the load increased to 13 kip, an

additional three cracks were developed: One at the midspan, and the other two cracks at the

49

location of the applied load. Four more flexural cracks located in the constant shear region

were initiated at an applied load of 17 kips, as illustrated in Figure 4.4. At this level of load,

the existing cracks rapidly progressed toward the compression zone of the beam as the load

continued to increase.

At an applied load of 26 kips, three minor flexural cracks appeared in the constant

shear region near the supports. Yielding occurred at a load of 34 kips. At this stage, no more

cracks were formed; however, existing cracks widened due to the crack stabilization

phenomenon due to yielding of the steel and the shifting of the neutral axis. This is a

common behavior in concrete section reinforced with mild steel. The specimen continued to

maintain the applied load up to 40 kips where failure suddenly occurred. The failure was due

to crushing of the concrete when the concrete strain reached the ultimate strain. Distress of

concrete was observed near the load location on the compression side. Figure 4.5 shows the

crushing of the concrete at 40.7 kips. Beam B1 functioned satisfactory and did not

experience any premature failure due to shear or debonding between the concrete and steel.

4.3.2 Crack Pattern

The crack pattern of the control specimen can be seen in Figure 4.6. A total of 16

cracks were observed in Beam B1. The crack pattern associated with Beam B1 consisted of

14 flexure cracks and two flexure-shear cracks. Two flexure-shear cracks were located

immediately at each of the loading points. Seven major vertical cracks were observed in the

constant moment region, while nine minor cracks were found in the constant shear region.

All cracks initiated from the bottom and then propagated upward to the top of the beam.

50

Crack spacing ranged from 8 to 10 inch along the beam. Cracks were developed at

approximately the location of the stirrups; therefore, it was evident that the spacing of cracks

was primary controlled by the location of the stirrups.

Cracks at the constant moment region occurred at the earlier stage and continued to

propagate after the yielding of the steel. On the other hand, cracks located within the

constant shear region initiated at the later stage. As the applied load exceeded the yielding

point, continuous increasing of the crack width was observed.

4.3.3 Crack Width

Crack behavior was monitored only in the constant moment zone. A crack

comparator was used to measure the crack width at the location of the applied load. The

load-crack width behavior of Beam B1 as shown in Figure 4.7 consisted mainly of two

portions: crack width before yielding of the reinforcement, and the crack width after yielding

of the steel including the behavior prior to failure load.

At the first stage of the load-crack width behavior, hairline cracks were observed

through out the specimen. The crack width ranged from 0.01 to 0.025 inch. The second

stage reflected continuous increasing of the crack width, which resulted from yielding of the

steel. The crack width at this stage ranged from 0.025 to 0.19 inches prior to failure.

4.3.4 Deflection

The maximum deflection in Beam B1 was measured at midspan. The load-midspan

deflection behavior of beam B1 is shown in Figure 4.8.

51

The load-midspan deflection behavior of beam B1 showed that the deflection

increased linearly with an increase of the applied load, up to the cracking load of 8.5 kips.

After cracking, the specimen experienced 75 percent stiffness reduction and continued to

behave linearly up to the yield load at 35 kips. At this stage, most of the cracks in the section

were initiated and started to propagate towards the compression zone. After yielding, the

specimen experienced significant loss of stiffness accompanied by significant deflection. The

beam underwent strain-hardening effect before reaching the ultimate flexural strength of 40.7

kip. The total deflection after yielding of reinforcement was about 75 percent of the total

deflection. The maximum deflection at midspan at the failure was 3.8 inches.

4.3.5 Ultimate Flexural Capacity and Failure Mode

The measured load at failure was 40.7 kips. The measured tensile strain of the Grade

60 steel rebar prior to the crushing of the concrete was 0.020 in/in as shown in Figure 4.9.

The stress level in steel corresponding to the maximum load was significantly higher than at

the yielding strength; therefore, this behavior indicated that the steel was in the range of

strain hardening prior to crushing of the concrete.

Crushing of concrete occurred at the top of the beam and corresponded to a strain of

0.004 in/in as shown in Figure 4.10. The failure of the Beam B1 was classified as ductile

flexural failure, due to the yielding of the tension reinforcement prior to crushing of the

concrete. No bond or other type of failure was observed during the time of testing. Shear

cracks were visible at a high load level. Failure occurred on the top fiber of the section at the

location of the applied load. The failure mode of the control beam was due to crushing of the

52

concrete in the compression zone after the considerable deflection and yielding of

reinforcement.

4.4 BEHAVIOR OF BEAM B2

Beam B2 was the second beam tested under the static loading conditions. This beam

was reinforced with two top # 4 Grade 60 steel bars and two bottom # 6 MMFX bars in the

tension side. The beam was loaded monotonically to failure using the 440 kips closed loop

MTS system. The observed behaviors and experimental result of Beam B2 are reported and

discussed in this section.


Similar to the Beam B1, the measured cracking load of Beam B2 was at 8.5 kips.

Two flexural cracks appeared within the constant moment region, one at 12 inch from each

of the applied load location within the constant moment zone. At 11 kips, four additional

cracks developed outside of the constant bending zone. At an approximate load of 13 kips,

three additional flexural cracks were initiated: one at the load location, and two occurred

outside of the loading zone within the shear span. Cracking at the early stages is shown in

Figure 4.11.

Initiation of two flexural-shear cracks occurred at the load level of 17 kips. Both

cracks appeared just outside of the constant moment region. Two additional flexural-shear

cracks located at three feet from the support appeared at an applied load of 20 kips.

53

Three more shear cracks appeared at a load of 26 kips, 37 kips, and 40 kips

respectively. All shear cracks developed within the constant shear region and were located

near the support. At this load stage, the beam was extensively cracked and the crack width

significantly widened.

Crushing of the concrete occurred at an applied load of 54.7 kips. Failure of the

concrete was observed at the location of the applied load on the compression side, as shown

in Figure 4.12. After the ultimate load, the load was dropped to 50 kips and the flexural

crack located at 1 foot from the right point load propagated to the top towards the

compression zone where crushing of the concrete magnified. The beam was severely

cracked accompanied by extensive deformation prior to failure. Figure 4.13 shows failure of

Beam B2 due to crushing of the concrete.

4.4.2 Crack Pattern

Crack pattern associated with Beam B2 is shown in Figure 4.14. A total of 23 cracks

were observed in beam B2. Cracks pattern of Beam B2 consisted of eleven flexural cracks,

and twelve flexural-shear cracks. Five major flexural cracks were observed in the constant

moment region. Flexural cracks occurred first, followed by flexural-shear cracks, and finally

shear cracks in the constant shear zone. All flexural cracks were vertical, as expected, and

occurred just inside the constant moment zone. Flexural-shear cracks initiated vertically and

then deviated diagonally. Some of the flexural cracks within the shear span propagated

diagonally upward toward the applied loads. The locations and spacing of the cracks were

54

influenced by the locations of the stirrups. Flexural cracks were wider in width, while shear

cracks were considerably less crack wide.

4.4.3 Crack Width

Similar to control specimen reinforced with Grade 60 steel (Beam B1), crack

characteristics of the beam were monitored only within the constant moment region. The

load-crack width relationship shown in Figure 4.15 is initially linear and become non-linear

due to formation of more cracks by the increased applied load. The linear portion began at

the initiation of the first flexural crack at an applied load of 8 kips and continued to increase

with respect to applied load. At an applied load of 25 kips, hairline cracks were observed

throughout the beam. The crack width in this stage ranged from 0.01 to 0.025 inch. As the

load increased, the load-crack width relationship became non-linear and continued up to the

ultimate load of 54.7 kip. During this stage, existing cracks were widened and new cracks

were formed. The crack width corresponding to the non-linear stage ranged from 0.025 to

0.12 inches.

4.4.4 Deflection

The maximum deflection occurred at the midspan location was measured by two

LVDTs. The load-midspan deflection shown in Figure 4.16 illustrates that the beam

reinforced with two # 6 MMFX did not exhibit any yielding plateau. The load-deflection

behavior lacked the classical yielding behavior of the beam reinforced with mild steel.

55

Prior to the initiation of first cracking load of 8 kips, the deflection increased linearly

with an increase of the applied load. The beam underwent major stiffness loss of about 80

percent as the cracks development quickly progressed from the constant moment region into

the constant shear region. The beam stiffness was reduced from 165.5 kip/in to 26.2 kip/in

after the development of first flexural crack. The load-deflection of Beam B2 continued to

behave linearly up to 37 kips where the second loss of beam stiffness occurred. During this

stage, the concrete section was severely cracked. Existing cracks propagated towards the

compression zone and the width of the cracks significantly increased. Ninety-three percent

of stiffness deterioration was observed at this point. Beam B2 functioned satisfactory with

no sign of bond or shear failure as the applied load approached 50 kips. The ductility of the

beam was clearly exhibited as the specimen experienced significant deformation, and crack

development, while maintaining more flexural load. The beam continued to sustain more

load and failed by crushing of the concrete which occurred at an applied load of 54.7 kips.

The deflection corresponding to the maximum load was 3.1 inches and increased to 4 inches

at unloading. It was decided to unload the beam due to safety reasons at the load level of 50

kips.


As described earlier, the ultimate load of Beam B2 prior to failure was 54.7 kips.

Strain gage attached to the surface of the reinforcing rebars were damaged at a strain level of

approximately 0.005 in/in, therefore the strain in the MMFX rebar was evaluated based on

the measured concrete strain at the level of the reinforcement by assuming a perfect bond

between the steel and concrete. As seen in Figure 4.17, the ultimate flexure strength

56

occurred in the MMFX rebar at a tensile stress of 0.0098 in/in. The strain corresponded to

the tensile stress of the MMFX rebar of 146.3 ksi, which indicated that the MMFX rebars did

not reach the ultimate strength and failure occurred due to crushing of the concrete.

Crushing of concrete at the top of the section occurred at the concrete strain of 0.0029

in/in, as shown in Figure 4.18. The failure of Beam B2 was classified as ductile flexural

failure due to the large measure of strain of the reinforcement bars followed by the crushing

of the concrete at failure. No bond failure was observed during the experiment. Flexural-

shear cracks were visible only after 28 kips of load. Failure suddenly occurred as crushing of

the concrete located at the point load was accompanied by the sudden propagation of a major

flexural crack at the location of the applied load.


Beam B3 was the third beam in this experimental program tested under a static

loading condition. This beam was reinforced with two # 4 Grade 60 steel as compression

reinforcement and three # 6 MMFX in the tension side. The beam was loaded monotonically

to failure using the closed loop 440 kip MTS system. The observed behaviors and

experimental result of Beam B3 are discussed in the following section.


The initial flexural cracking of Beam B3 occurred within the constant moment region

at a load of 10 kips. Three flexural cracks initiated at the load level of 11 kips: one located

at each concentrated load, and another located at midspan. At about 12 kips, two additional

57

cracks were formed at the bottom of the beam just outside of the constant moment region.

Within 20 kips, 9 more cracks started to form in the constant shear region. Crack behavior at

an early stage of loading is illustrated in Figure 4.19.

At approximately 40 kips, a series of flexural-shear cracks were formed just

immediately out side of the applied load locations. Existing cracks located outside of the

loading zone began to deviate from vertical cracks into diagonal cracks due to the presence

of high shear. Splitting cracks occurred at the constant shear region. At this point, the

existing cracks propagated upward as the applied load further increased. There was no sign

of excessive deflection or severe crack width at this point.

At a load of 50 kips, two shear cracks initiated at about two feet from each of the

supports. Four additional flexural cracks appeared at loads of 53, 55, 60, and 69 kips, all

inside the constant moment region. As the applied load approached 70 kips, a number of

minor cracks joined the flexural shear cracks and deviated diagonally into shear cracks. At

this point, the beam was severely cracked accompanied with a large deformation. In

addition, propagation of flexural and shear cracks throughout the beam became much more

evident, as seen in Figure 4.20.

The failure of Beam B3 occurred at an applied load of 77.9 kips. The specimen failed

by crushing of the concrete. The location of the failure was observed at about one foot from

the right applied load. Significant distress due to high compressive stress induced by a high

load is evident in Figure 4.21.

58

After the ultimate load, Beam B3 continued to sustain the 73 kips of loading. The

failure of the Beam B3 was similar to the failure of Beam B1 and Beam B2; however,

crushing of the concrete of Beam B3 was less severe in comparison to Beam B2, Figure 4.21.

There were no sign of bond failure or any other type of premature failure associated with this

beam.

4.5.2 Crack Pattern

Beam B3 had similar crack patterns to Beams B1 and B2. A total of 32 cracks were

found in Beam B3. Twenty-two were major cracks and eight were minor cracks. The crack

pattern consisted of five major flexural cracks in the constant moment region, 17 flexural-

shear cracks in the constant shear region, and 8 minor flexural cracks throughout the beam.

Similar crack sequences of Beam B2 were also observed in Beam B3: flexural cracks

occurred first; flexural-shear cracks occurred second, and the shear cracks occurred last.

Crack pattern associated with this beam are illustrated on Figure 4.19.

4.5.3 Crack Width

The behavior of loading and the crack width of Beam B3 is shown in Figure 4.22. After the

initiation of the first crack, the crack width behaved in a non-linear fashion with respect to

the applied load. After the load level of 55 kips, existing crack width monitored at the right

point load began to widen, and the existing cracks began to propagate upward toward the

compression zone. This behavior continued until the beam reached its failure load of 77.9

kips. The crack width corresponding to the failure load was 0.062 inch.

59

4.5.4 Deflection

The load-midspan deflection behavior of Beam B3 exhibited similar behavior to that

of Beam B2. The load-deflection curve illustrated in Figure 4.23 consisted of linear behavior

up to the initiation of the first crack at 10 kips. The beam experienced stiffness reduction of

73 percent, as the stiffness was reduced from 168.6 kip/in to 41.5 kip/in after the initiation of

the first flexural crack. The beam continued to exhibit linear behavior up to a second

stiffness reduction at the load level of 55 kips. At about 55 kips, the beam was totally

cracked with flexural, flexural-shear, and shear cracks.

After the second stiffness reduction of 88 percent, the beam experienced non-linear

behavior induced by the significant straining of MMFX rebars. The beam maintained the

flexural load capacity up to the ultimate load of 77.9 kips. The measured deflection

corresponding to the ultimate load was 2.7 inch. Immediately after the failure, the loading

was dropped from 77.9 kips to 72 kips as the specimen lost most of the original stiffness due

to crushing of the concrete. The beam was unloaded when the deflection reached 2.95

inches.


The measured maximum strain of the concrete at the level of the reinforcement was

0.0091 in/in as evident in Figure 4.24. This strain corresponded to a stress in the MMFX

rebars of 140.02 ksi, which exceeded the off-set yield strength of 120 ksi. Beam B3 had the

highest flexural capacity (77.9 kips), smallest crack width, and smallest midspan deflection

among the beams tested under static conditions. Nevertheless, the specimen suffered a

60

crushing of concrete failure when the concrete strain reached the rupture value of 0.0032

in/in, as seen in Figure 4.25.


Beam B4 was the forth beam tested in this experimental program. This beam had the

same reinforcement as Beam 3. The beam was loaded and unloaded for 15 cycles under slow

cyclic configuration using the stroke control option on the 440 kip capacity closed loop MTS

system. The observed behaviors and the experimental results of Beam B4 are reported and

discussed in this section.


The initial cracking of Beam B4 occurred at the first loading cycle (Pmin = 0 kip, Pmax

= 25 kip). Three flexural cracks simultaneously initiated the beam just inside of a constant

moment region at a load level of 11 kips. At about 15 kips six additional cracks appeared in

the beam: three cracks inside the constant moment region, and another three cracks just

inside the constant shear region. As the applied load approached 18 kips, two flexural cracks

formed about 2 feet inside of the constant shear region. At 20 kips, two additional crack

initiated further inside the constant shear region. Toward the end of the first loading cycle, at

a load level of 25 kips, no more cracks were formed. The existing hairline cracks propagated

towards the compression zone. The early stages of cracking are shown in Figure 4.26.

During the second and third cycle, there was no formation of new cracks. The exited cracks

remain unchanged, and no propagation was observed.

61

As the loading approached the load level of 27 kips, two additional cracks initiated in

the middle of constant shear region. At about 34 kips, two more flexural cracks developed

near the midpoint of the constant region. As the load increased to 36 kips, four more cracks

located inside the middle of constant shear zone began initiation. As the load approached the

end of the forth load cycle at 42.5 kips, no additional cracks were formed. During the fifth

load/unload cycle, no more cracks were formed until the applied load reached 41 kips. At

approximately 41 kips, shear cracking was observed at about two feet away from each

support. As the load increased to the end of the fifth cycle (Pmin = 0 kip, Pmax = 42.1 kip), the

existing flexural-shear cracks began to deviate diagonally at angle range between 30 to 45

degree. No additional cracks were observed at the beginning or at the end of the sixth

loading cycle. Existing cracks remained stable to the end of the fifth and sixth loading cycle.

As the load approached 45 kips on the seventh loading cycle (Pmin = 0 kip, Pmax =

55.8 kip), four minor cracks were observed: one crack occurred inside the constant moment

region, while the three other cracks occurred just inside of the constant shear region. A series

of splitting located just outside of the constant moment region began to develop at 52 kips.

Toward the end of the seventh loading cycle at 55 kips, existing cracks located in the middle

of the constant shear region were accompanied by a series of splitting cracks and then turned

into shear cracks.

At the eight loading cycle (Pmin = 0 kip, Pmax = 55.8 kip), one shear crack initiated the

section at the approximated load of 47 kips. As the beam reached the end of the loading

62

cycle, three additional shear cracks initiated at about 55 kips near supports. Existing cracks

significantly propagated in the upward fashioned toward the top of the concrete section.

During the ninth loading cycle (Pmin = 0 kip, Pmax = 55.8 kip), two additional shear

cracks were initiated at the applied load level of 55 kips. Existing shear cracks began to

propagate diagonally at an angle, while the existing shear cracks located inside the moment

zone remained unchanged.

During the tenth, eleventh, and twelfth loading cycle (Pmin = 0 kip, Pmax = 65.7 kip),

splitting and shear cracks developed about 2 feet inside the shear region at the loading. At

approximately 60 kips, a shear crack initiated at the location of left support. As the load

increased to 61 kips, a flexural crack was formed just outside the left of the loading zone. As

the applied level reached the end of the twelfth cycle at 65.7 kips, existing shear cracks near

each support showed significant propagation. At this point, the beam was extensively cracks

accompanied with large deformation. Later stages of cracking are shown in Figure 4.27.

During the last three loading cycles (Pmin = 0 kip, Pmax = 72.6 kip), the beam was

loaded up to 72.6 kips. One shear crack initiated at the thirteenth cycle at a load of 60 kips.

During the later stage of the fourteenth loading cycle, the monitored crack began significant

widening due to straining in MMFX rebar.

At the last loading cycle, the fifteenth cycle (Pmin = 0 kip, Pmax = 72.6 kip),, Beam B4

experienced significant deformation as the load approached 65 kips. At 70 kips, flexural-

63

shear cracks located at each support progressed toward the top of the beam. A similar

phenomenon was also observed by the flexural cracks located inside the constant moment

region. At 70 kips of applied load, the beam experienced a serious degree of crack growth.

The Beam B4 continued to carry a load of 72.6 kips toward the end of the fifteenth cycles.

Crushing of the concrete at the location of applied load began at the beginning of the

unloading process at the fifteenth cycle, as shown in Figure 4.28. The failure was classified

as ductile failure as evident from the significant straining of steel preceding the rupture of the

concrete. The crushing of the concrete of Beam B4 has similar severity levels in comparison

to Beam B3.

4.6.2 Crack Pattern

Beam B4 had similar crack patterns to Beam B3 due to the same reinforcement

configuration. Beam B4 had a total of 34 cracks: 26 were major cracks and 8 were minor or

splitting cracks. Crack patterns associated with this beam consisted of 8 major flexural

cracks located in the constant moment region, 18 flexural-shear/shear cracks located in the

constant shear region, and 8 minor/splitting cracks located through out the beam. Similar to

B3, flexural cracks occurred at the lower load level, flexural-shear cracks occurred at higher

load level, and shear cracks occurred last at a very high load level.

4.6.3 Crack Width

Crack width information of Beam B4, displayed in Figure 4.29, was monitored

through out the fifteen load-unload cycles. Load-crack width was recorded at the beginning

and the end of every three load-unload cycle.

64

As seen in Figure 4.29, Beam B4 had a similar load-crack width relationship with an

equally reinforced Beam B3. The only difference lied on crack growth at the end of every

three load-unload cycles. An increase of crack width of 0.003, 0.003, 0.007, and 0.014 inch

was measured at the end of the third, sixth, ninth, and twelfth cycle, respectively. As the

numbers indicated, the crack width became more pronounced as the loading progressed. The

crack growth of 0.014 inches recorded at the end of the twelfth cycle was approximately

three times higher than a crack growth of 0.003 inches recorded at the end of the third cycle.

This behavior was attributed to a deterioration of stiffness due to nature of slow cyclic

loading configurations. The maximum crack width of 0.06 inches was recorded at the

beginning of the fifteenth loading cycle at an applied load of 72.6 kips.

4.6.4 Deflection

The load-midspan deflection behavior of Beam B4 demonstrated in Figure 4.30 was

also similar to the behavior of Beam B3. Prior to initiation of first crack, the deflection

increased linearly with the applied load. The beam experienced its first stiffness reduction of

76 percent, as the measured stiffness reduced from 188.1 kip/in to 43.8 kip/in. After the first

three load-unload cycle, Beam B4 experienced the second stiffness loss of around 3 percent,

as the measured stiffness went from 43.7 kip/in to 42.42 kip/in. The beam continued to

behave linearly as the applied load reached 42 kips at the end of sixth load-unload cycle. At

the beginning of the ninth load-unload cycle, a minor stiffness loss due to the nature of load-

unload cycle was measured at 34.4 kip/in, a reduction of 82 percent from the pre-cracking

stage. Beam B4 experienced the forth stiffness reduction, as the stiffness was reduced from

34.4 kip/in to 22.7 kip/in at the beginning of the tenth load-unload cycle. A significant

65

reduction of 88 percent from the gross stiffness was clearly observed at the load level of 60

kips, where the midspan deflection of 1.6 inch was measured at the end of the twelfth load-

unload cycle. At an approximate load of 60 kips, the beam was covered with numbers of

flexural, flexural-shear, and shear cracks. The last stiffness reduction occurred as the beam

began the thirteenth load-unload cycle. At an approximate load of 65 kips, the section

stiffness was 17.6 kip/in, a 171.4 kip/in reduction from the initial stiffness. At this stage, the

beam experienced large deformation at midspan. Significant straining of the reinforcing steel

beyond the off-set yield point was clearly observed as existing cracks began to increase at a

much higher rate. The beam maintained the flexural load capacity up to the end of the

fifteenth load cycle. Crushing of the concrete was observed at the early stage of unloading at

the fifteenth cycle. The beam failed at the maximum applied load of 72.6 kips. Beam B4

continued to resist the applied load of 70 kips due to the high-strength properties of the

MMFX steel. The beam was unloaded at the deflection of 3.2 inches.


Beam B4 had the second highest ultimate flexural capacity of 72.6 kip in this

experimental program. At the end of the fifteenth cycle, a significant straining of the MMFX

rebars in neighborhood of 0.0095 in/in was observed in Figure 4.31. The maximum stress in

the rebar corresponding to the maximum load was captured at 141.95 ksi. The beam

functioned satisfactory as the crushing of the concrete occurred at the concrete strain of

approximately 0.004 in/in, as seen in Figure 4.32. Crushing of the concrete at the location of

the point loads on Beam B4 was slightly more pronounced when compared to Beam B3. The

66

failure was classified as ductile flexural failure. No bond or shear failure was observed in the

beam.

67

Table 4.1: Compressive strength of the concrete

Batch 1 Batch 2 Cylinder Compressive Strength (psi) Compressive Strength (psi)

C1 6861 6997 C2 7036 6915 C3 7078 7069 C4 7003 7345 C5 7008 7227 C6 7296 7192

C average = 7047 7244 Std. Deviation = 129.8 330.8

Table 4.2: Tensile strength of the concrete Batch 1 Batch 2

Cylinder Tensile Strength (psi) Tensile Strength (psi) S1 589 520 S2 588 535

S average 588.5 527.5 Std. Deviation = 0.5 7.5

68

Table 4.3: Results from tension test of reinforcements (* specimen did not load to failure, # calculated at 60 ksi stress)

#6 MMFX (Batch 1) Proportional Young's Yield Strength Strain at 0.2% Strain at Ultimate Strain at Stress at Strain at

Test # Limit Strength Modulus of at 0.2% offset offset yield 80 ksi Strength Ultimate Failure Failure (ksi) Elasticity (ksi)# (ksi) Strength (in/in) stress (ksi) Stress (in/in) (ksi) (in/in)

1 84.33 27847 125.02 0.0064 0.00324 178.59 0.0558 125.89 0.2033 2 86.57 26382 121.35 0.0063 0.00302 178.79 0.0557 131.99 0.1987 3 82.41 28301 125.28 0.0065 0.00317 177.45 0.0487 121.08 0.1859

Avg. 84.44 27510 123.88 0.00640 0.00314 178.28 0.0534 126.32 0.1960 St. Dv. 2.08 1003.53 2.20 0.00010 0.00011 0.72 0.0041 5.47 0.0090

#6 MMFX (Batch 2) Proportional Young's Yield Strength Strain at 0.2% Strain at Ultimate Strain at Stress at Strain at

Test # Limit Strength Modulus of at 0.2% offset offset yield 80 ksi Strength Ultimate Failure Failure (ksi) Elasticity (ksi)# (ksi) strength (in/in) stress (ksi) Stress (in/in) (ksi) (in/in)

1* 84.28 27514 122.51 0.0064 0.0031 180.08 0.0514 177.32 0.0563 2* 84.07 28434 128.57 0.0065 0.003 180.53 0.0519 172.71 0.0172 3 Damage at the time of testing

Avg. 84.18 27974 125.54 0.0065 0.0031 180.31 0.0517 175.02 0.0367 St. Dv. 0.15 650.76 4.29 0.0001 0.0001 0.32 0.0004 3.26 0.0277

#6 Grade 60 tension steel Young's Yield Strength Yield Strain Ultimate Strain at Stress at Strain at Strain at

Test # Modulus of (ksi) (in/in) Strength Ultimate Failure Failure Hardening Elasticity (ksi) (ksi) Stress (in/in) (ksi) (in/in) (in/in)

1 26708 64.10 0.0024 96.61 0.1190 90.94 0.1440 0.0118 @ 65 2 28750 63.25 0.0022 96.39 0.1556 93.21 0.1556 0.0116 @ 64.28 3 26358 63.26 0.0024 96.33 0.1200 90.70 0.1855 0.0117 @ 64.23

Avg. 27272 63.54 0.0023 96.44 0.1315 91.62 0.1617 0.0117 @ 63.9 St. Dv. 1291.7 0.49 0.0001 0.15 0.0208 1.39 0.0214 0.0001 @ 1.33

#4 Grade 60 compression steel and stirrup Young's Yield Strength Yield Strain Ultimate Strain at Stress at Strain at Strain at

Test # Modulus of (ksi) (in/in) Strength Ultimate Failure Failure Hardening Elasticity (ksi) (ksi) Stress (in/in) (ksi) (in/in) (in/in)

1 25442 61.06 0.0024 92.32 0.1135 90.30 0.1550 0.0134 @ 62.44 2 27522 63.30 0.0023 96.39 0.1190 90.30 0.1550 0.0116 @ 64.28 3 24435 63.66 0.0026 91.66 0.1343 83.96 0.1900 0.0139 @ 63.84

Avg. 25816 62.67 0.00243 93.46 0.1223 88.19 0.1667 0.0129 @ 63.52 St. Dv. 1552.78 1.41 0.00015 2.56 0.0108 3.66 0.0202 0.00121 @ 0.96

69

Figure 4.1: Stress-strain relationship for concrete

Figure 4.2: Stress-strain relationship for #4 Grade 60 compression reinforcement

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020

Axial Strain (in/in)

Stre

ss (p

si)

0

10

20

30

40

50

60

70

80

90

100

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

Strain (in/in)

Stre

ss (k

si)

70

Figure 4.3: Stress-strain relationship for #6 Grade 60 and MMFX tension reinforcements

Figure 4.4: Initial stage of loading on Beam B1

#6 Grade 60 Steel

#6 MMFX Steel

0.2%0

20

40

60

80

100

120

140

160

180

200

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20Steel Strain (in/in)

Stre

ss (k

si)

71

Figure 4.5: Crushing of Concrete in Beam B1

Figure 4.5: Crushing of concrete on Beam B1

Figure 4.6: Crack pattern on Beam B1

Crushing of the concrete

72

Figure 4.7: Load-crack width information on Beam B1

Figure 4.8: Load-midspan deflection of Beam B1

0

5

10

15

20

25

30

35

40

45

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Midspan Deflection (in)

Load

(kip

)

0

5

10

15

20

25

30

35

40

45

0 0.05 0.1 0.15 0.2Crack Width (in)

Load

(kip

)

73

Figure 4.9: Load-steel strain of Beam B1

Figure 4.10: Load-concrete strain of Beam B1

0

5

10

15

20

25

30

35

40

45

0.000 0.005 0.010 0.015 0.020 0.025Steel Strain (in/in)

Load

(kip

)

@ top surface @ level of top steel @ mid-height @ level of bottom steel

0

5

10

15

20

25

30

35

40

45

50

-0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025

Concrete strain (in/in)

Load

(kip

)

74

Figure 4.11: Initial stage of cracking of Beam B2

Figure 4.12: Initiation of crushing of concrete of Beam B2

75

Figure 4.13: Failure mode of Beam B2 due to crushing of concrete


Crushing of the concrete

76

Figure 4.15: Load-crack width of Beam B2


0

10

20

30

40

50

60

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14Crack Width (in)

Load

(kip

)

0

10

20

30

40

50

60

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Midspan Deflection (in)

Load

(kip

)

77



0

10

20

30

40

50

60

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Steel Strain (in/in)

Load

(kip

)

@ top surface@ level of top

steel @ mid-height@ level of bottom

steel

0

10

20

30

40

50

60

-0.010 -0.005 0.000 0.005 0.010 0.015 0.020

Concrete Strain (in/in)

Load

(kip

)

78

Figure 4.19: Initial stage of cracking on Beam B3


79

Figure 4.21: Failure mode of Beam B3


Crushing of concrete

0

10

20

30

40

50

60

70

80

90

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09Crack Width (in)

Load

(kip

)

80



0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5


Load

(kip

)

0

10

20

30

40

50

60

70

80

90

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014Steel Strain (in/in)

Load

(kip

)

81


Figure 4.26: Initial stage of cracking on Beam B4

@ top surface

@ level oftop steel

@ mid-height @ level of bottom steel

0

10

20

30

40

50

60

70

80

90

-0.01 -0.005 0 0.005 0.01 0.015


Load

(kip

)

82

Figure 4.27: Later stage of crack on Beam B4

Figure 4.28: Failure mode on Beam B4

Crushing of the concreteCrushing of the concrete

83



0.04

2 to

0.0

56 @

65.

7k

0.01

4 to

0.0

17@

25k

0.02

1 to

0.0

24 @

42k

0.03

3 to

0.0

4 @

55k

0.06, 72.6k

0

10

20

30

40

50

60

70

80

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Crack Width (in)

Load

(kip

)

0

10

20

30

40

50

60

70

80

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Midspan Deflection (in)

Load

(kip

)

84



0

10

20

30

40

50

60

70

80

90

0.000 0.005 0.010 0.015 0.020 0.025


Load

(kip

)

@ top surface

@ level oftop steel

@ mid-height @ level of bottom steel

0

10

20

30

40

50

60

70

80

-0.0100 -0.0050 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Concrete strain (in/in)

Load

(kip

)

85

CHAPTER 5

DISCUSSION OF EXPERIMENTAL RESULTS AND ANALYTICAL PREDICTION

5.1 GENERAL

Discussion of the experimental results and the analytical models used for the

prediction of behavior are presented in detail within this chapter. The first portion of this

chapter discusses the experimental result, while the second portion evaluates the accuracy of

the analytical model used in the prediction of the beams tested under static loading

conditions. This chapter also presents the effects of various parameters, including the effect

of the reinforcement ratio of MMFX on the behavior, in order to provide general design

recommendations for the use of MMFX as reinforcement for concrete structures.

5.2 FLEXURAL BEHAVIOR

To evaluate the structural behavior of the tested beams in this experimental program,

information on load-midspan deflection, load-steel strain, and load-concrete strain are

explained in detail for each beam in Chapter 4.

In general, results for all tested beams exhibit an ample warning through large

deformation, which is evident by significant straining in both the MMFX and Grade 60 steel

rebar before failure. All beams function satisfactorily according to the new “unified”

minimum ductility required by ACI 318-02. The summaries of the experimental values for

all of the tested beams are reported in Table 5.1. In this section, beam behaviors are

compared in order to study the effect of using MMFX versus Grade 60 steel rebars.

86

5.2.1 Beam B1 vs. Beam B3

To evaluate the flexural response of concrete beams reinforced with MMFX rebars,

load-midspan deflection in Beam B3 was compared to the behavior of the beam reinforced

with A615 Grade 60 steel, Beam B1, which was reinforced with the same tension

reinforcement ratio.

As evident in Figure 5.1, the load-midspan deflection behaviors of the two beams

show that deflection increases linearly with an increase in the applied load prior to cracking.

After the initiation of the first crack, which occurred at the approximate load level of 8.5

kips, Beam B1 and Beam B3 experience similar magnitude of stiffness reduction. This

behavior is attributed to the same elastic modulus value for the two reinforcing materials and

the same reinforcement ratio. As the load continued to increase, the Grade 60 beam behaved

as expected by showing signs of yielding of the reinforcement at the load of 33 kips and at

the midspan deflection of 0.7 inches followed by significant deformation with the slight

increase in the applied load. In contrast, the MMFX reinforcing beam did not exhibit any

yielding characteristics. Beam B3 continued to maintain the original stiffness up to a load

level of 50 kips, where a stiffness reduction occurred.

Failure loads of Beam B1 occurred at 40.7 kips due to strain hardening of Grade 60

steel reinforcement. The deflection at ultimate load was measured at 3.87 inches while the

ultimate steel strain was recorded at 2.01 percent, as shown in Figure 5.2. The ultimate load

of Beam B3 was 77.9 kips, which occurred at a 2.7 inch deflection. In comparison to the

beam reinforced with Grade 60 steel, the maximum load of the equally reinforced MMFX

87

beam was 90 percent higher. The measured ultimate strain in the MMFX rebar (εs = 0.0091

in/in) was 50 percent less than the ultimate steel strain of the Grade 60 steel; however, it

exceeded a minimum ductility requirement (εs = 0.005 in/in) ACI 318-02. This behavior

suggests that beams with equal reinforcement ratios, like the one reinforced with MMFX,

will exhibit less ductility than the with Grade 60 steel. This simulates the behavior of

structural members with higher reinforcement ratios.

After reaching the ultimate load, the load carrying capacity of the beam reinforced

with the MMFX beam was reduced from 77.9 kip to 74.2 kips. The beam continued to resist

the 74.2 kips applied load until the decision was made to unload the beam at a deflection of

2.95 inches. This was done for safety reasons and to avoid causing damage to the

instrumentation. The maximum steel stress in the MMFX rebar was 140.02 ksi, which

corresponded to 0.9 percent steel strain. The measured strain suggests that the MMFX rebar

did not reach its maximum capacity and failure of the beam was due to the crushing of the

concrete. It is reasonable to assume that the beam with MMFX reinforced steel would still

be capable of achieving higher section ductility if the load had not terminated. It should be

noted that prior to failure the two beams, Beam B1 and Beam B3, provide an ample warning

by showing a large deflection and a series of extensive cracks.


To utilize the high strength characteristics of the MMFX steel, the flexural

performance of a lower reinforcement ratio was used for Beam B2 and compared with the

higher reinforcement ratio used for Beam B3. The reinforcement ratio used for Beam B2

88

was 0.47 percent while 0.704 percent was used for Beam B3. Both specimens were

reinforced in the tension side using #6 MMFX steel rebar.

The load-midspan deflection curves for both beams B2 and B3, which were

reinforced with MMFX steel, are given in Figure 5.3. The behavior is linear up to the

initiation of the first crack and non-linear with lower in stiffness in beam B2 until failure.

The cracking load for the lower reinforced beam, Beam B2, occurred at 8 kip, while the

cracking load for the higher reinforced beam, Beam B3, occurred at a slightly higher load of

10 kip. Beam B2 exhibits higher stiffness reduction. The stiffness loss after cracking was 84

and 75.4 percent for Beam B2 and Beam B3 respectively. Higher reduction in the stiffness

was primary influenced by the lower reinforcement ratio used in Beam B2. As the load

continued to increase, both beams continued to behave non-linear up to failure. This non-

linear behavior is inherited from the non-linearity of the material properties of the MMFX

rebar.

At a load level of 40 kips, Beam B2 suffered additional stiffness reduction as the

stiffness dropped from 165.5 kip/in to 26.2 kip/in. The second stiffness reduction had a high

severity level, as the midspan deflection was more prominent. Beam B3 continued to

maintain an excellent load carrying capacity until the second stiffness reduction occurred at a

load level of 50 kips. This behavior suggests that the increase in the reinforcement ratio of

MMFX rebar resulted in an increase of the overall stiffness of the beam. This relationship

follows the classical theory of reinforced concrete using mild steel reinforcement.

89

The maximum load of Beam B2 occurred at a load level of 54.7 kips with a

corresponding deflection of 3.1 inches, while the ultimate load of Beam B3 occurred at 77.9

kips and at a corresponding deflection of 2.7 inches. The results indicate that a beam with a

lower reinforcement ratio has lower strength and higher ductility than a beam with a higher

reinforcement ratio. The maximum measured strain in the MMFX rebar was approximately

1 percent, as shown in Figure 5.4, which is slightly more than what was measured for Beam

B3. After reaching failure, both beams experienced a drop in the load carrying capacity.

Beam B2 continued to behave in a manner similar to the characteristics of Beam B3 but

continued to carry less of a load. Beam B2 was unloaded at the deflection of 4.06 inches,

which corresponds to a steel strain of 1.79 percent. The steel strain of 1 percent at a

corresponding steel stress of 146.3 ksi was measured at the ultimate load of 54.7 kips. A

stress level of 164.88 ksi at the unloading point of the load confirms that the MMFX rebar

did not reach its strength of 178 ksi. The maximum measured strain of 146.3 ksi at ultimate

confirms that using lower reinforcing ratio fully utilized the high-strength potential of the

MMFX steel.


To assess the behavior of structural members reinforced with MMFX, Beam B4 was

tested under slow cyclic loading conditions. Beam B4 was reinforced with a reinforcement

ratio of 0.74 percent, similar to Beam B3, which was tested under static loading conditions.

Both rectangular concrete beams were reinforced with three #6 MMFX rebars on the tension

side.

90

The load-midspan deflection behavior of Beam B3 and B4 is shown in Figure 5.5. In

general, both beams exhibit similar load-midspan deflection behavior with exception of

Beam B3, which achieved higher flexural strength. Upon closer inspection, the load-

midspan deflection of Beam B4 can be classified into two phases: 1) The flexural behavior

at the early stage of cyclic loadings and 2) The flexural behavior at the later stage of loading.

The early stage of cyclic loading starts at the beginning of loading and continues to

the end of the 6th load cycle, which corresponding to the load level of 54 percents of the

ultimate capacity based on static test on the Beam B3. In this phase, Beam B4 closely

resembled the behavior of Beam B3. The midspan deflection on both beams increased

linearly in the pre-cracking stage with the increase of applied load. After the initiation of the

first crack, which occurred at a load level of 10 kips, both beams suffered the similar

magnitude of stiffness reduction. Beam B4 continued to follow the load-midspan deflection

path of Beam B3 without significant deterioration of stiffness. At the end of the 6th cyclic

load level of 42 kips, the midspan deflection of both beams was at 0.8 inch.

The later stage of cyclic loading starts at the beginning of 7th loading cycle and ends

at the failure of Beam B4. Up to the end of the 12th load cycle, 88 percent of the ultimate

load based on the static test of Beam B3, the load-midspan deflection of Beam B4 follow the

observed path of Beam B3. A continuous deterioration of stiffness is evident by a more

pronounced mid-span deflection after the end of the 12th, and 15th load/unload cycles. This

behavior is typical and can be observed in any concrete structure that is subjected to repeated

loading.

91

Due to the nature of repeated loading conditions, Beam B4 lost 7 percent in strength.

The deflection at ultimate for Beam B4 was 2.29 inches at 72.6 kips, which is 0.27 inch less

than Beam B3 at ultimate. Beam B4 was unloaded after a deterioration of 3.29 inches, which

corresponds to a load of 69.06 kips.

5.3 CRACK INFORMATION

In this section, cracking behavior for beams reinforced with MMFX are discussed and

compared to the beam reinforced with Grade 60 steel. Cracking behavior in this section is

presented in terms of crack patterns, number of cracks, and type of cracks.

The crack patterns at the failure of Beam B1, which was reinforced with Grade 60

steel, and the three beams reinforced with MMFX, Beam B2, B3, and B4, are illustrated in

Figure 5.7. It is evident that the cracks in the constant zone occurred at the early stage of

loading and are predominantly vertical flexural cracks. As the applied load increased, the

flexural cracks started to appear outside of the constant moment region. At a higher load

level, flexural cracks located within the constant shear region deviated diagonally and turned

into the flexural shear cracks. At approximately 75 percent of the ultimate loads of the three

MMFX beams, the shear cracks began to appear at 45-degree angle. All shear cracks were

located near the supports. A lower number of shear cracks in the Grade 60 beam, Beam B1,

is attributed to the low flexural capacity of the section. All cracks spaced out evenly and

ranged from 8 to 10 inches throughout the beam, which suggested that the position of the

crack is influenced by the location of the #4 Grade 60 stirrups.

92

Occurrences of cracks in Beam B1 at failure were almost 50 percent fewer than the three

beams reinforced with MMFX. For beams reinforced with MMFX, larger numbers of cracks

were observed for a total of 32 and 34 cracks for beams with a higher reinforced ratio, Beam

B3 and Beam B4, respectively, in comparison to 24 cracks for the beam with lower

reinforcement, Beam B2. Therefore, it can be concluded that more crack formations can be

expected for beams that have a higher reinforcement ratio Due to the characteristics of

MMFX, as the load increases more cracks are formed rather than widening the existing

cracks.

According to the load-crack width behavior in Figure 5.8, Beam B1 experienced a

significant degree of crack growth after significant yielding of the reinforcement rather than

having an increase in the number of cracks. The maximum crack width in Beam B1 was

more serious and was double in width in comparison to the maximum crack width in Beam

B3. Due to lower reinforcement, Beam B2 displayed larger crack widths at ultimate load in

contrast to the higher reinforcement ratio used for Beam B3. Beam B4’s load-crack

relationship closely matched that of Beam B3’s in the early stages of loading with the

exception of significant degrees of crack growth at the later stage of load and unload cycles.

5.4 FAILURE MODE

The failure mode of the four tested beams was due to the crushing of the concrete in

the constant moment zone after considerable deflection following yielding of the tension

reinforcement. The yielding of the reinforcement was observed in Beam B1 as the Grade 60

steel began yielding at the applied load of 34 kips. Similar behavior was observed in the

93

beams reinforced with MMFX rebars. The ultimate strain of the MMFX rebar was 0.98

percent in Beam B2, 0.91 percent in Beam B3, and 0.95 percent in Beam B4. The ultimate

strain of the MMFX rebars at failure surpassed the 0.2 percent offset yield strain of 0.61

percent, which corresponds to the rebar strength of 120 ksi. Concrete strain prior to the

crushing of concrete phenomenon occurred at 0.427 percent for Beam B1, 0.29 percent for

Beam B2, 0.324 percent for Beam B3, and 0.69 percent for Beam B4. A higher value of the

measured concrete strain in Beam B4 was due to the deterioration in the strength of concrete

after fifteen load and unloads cycles. The ultimate concrete strains are presented in Figure

5.9.

The severity levels of concrete crushing in the Grade 60 beam, Beam B1, and the

MMFX beam, Beam B3, are similar in magnitude. The lower reinforcement ratio of MMFX

used for Beam B2 exhibited a much more dramatic failure than Beam B3. Failure of Beam

B3 was much less dramatic and comparable with the failure that occurred in the Grade 60

Beam with the same reinforcement ratio. A more dramatic failure in Beam B2 was attributed

to 33 percent less tension reinforcement. Beam B4’s crushing of the concrete occurred after

the completion of the 15th load and unload cycles. The severity of the failure in Beam B4

was slightly higher but comparable to the equally reinforced Beam B1 and Beam B3. The

failure for all beams is shown in Figure 5.10.

It is important to report that all beams functioned satisfactorily and without any sign

of premature failure, such as bond or shear failure in any beam.

94

5.5 SERVICABILITY

In this section, crack width and deflection at the service loads of the tested beams are

evaluated and compared to the allowable ACI limits. The considered service load used in

this analysis was determined from the applied load that corresponded to 60 percent of the

yield strength of the tension reinforcement. Since the MMFX does not exhibit any yielding

plateau, the maximum allowable strength specified by the ACI (80 ksi) was used as the yield

strength for the MMFX rebars. Thus the experimental service load was evaluated at 20.5 kip

for Beam B1, 18 kip for Beam B2, and 21.40 kip for Beam B3. The serviceability evaluation

was performed only for the beams tested under static loading conditions.

The ACI allowable limits used were 0.0016 inch for maximum crack width, and 0.5

inch for maximum mid-span deflection. The limit for deflection was calculated based on

Equation 5.1.

360

lSL =∆ Eqn. 5.1

where,

∆SL = service load deflection

l = clear span length in inches

5.5.1 Deflection

The experimental load-midspan deflection curves for beams tested under static

loading are reported in Figure 5.11. As evident in Figure 5.11, the service load deflections

95

for all beams satisfy the ACI maximum deflection requirements of 0.5 inch with the service

deflections of Beam B1, B2, and B3. The lower deflection at service load is attributed to the

higher stiffness in Beam B3 and Beam B4 due to a higher reinforcement ratio than was used

for Beam B2.

5.5.2 Crack Width

The measured load-crack width relationship of Beam B1, B2, and B3 are presented in

Figure 5.12. Test results indicate that the measured crack width for Beam B1 and Beam B3

at service load condition falls below the 1999 ACI limit of 0.016 inch. The result also

indicates that Beam B2’s crack width at service load is about 20 percent higher than the

allowable limit due to lower reinforcement ratio used.

In order to comply with the ACI, the service load should be limited to compensate for

the lower stiffness due to the reduction of the reinforcement ratio selected, in order to utilize

the strength of MMFX. It is important to indicate that the excessive crack width of a lightly

reinforced MMFX concrete member may not affect the overall structural integrity due to the

highly corrosive-resistance of the MMFX rebar.

5.6 FLEXURAL ANALYSIS

In order to predict the behavior of the test beams, an analytical model using iterative

procedures was carried out in order to determine the flexural response of the concrete

section. Each beam was analyzed using strain compatibility approached in order to satisfy

the section equilibrium. This process was done to obtain moment and curvature relationship

96

at the mid-span section. The analytical model was based on the currently available concrete

theory, “layer-by-layer evaluation of the section force,” which utilizes the material

characteristics of the concrete and reinforcement, as described by Collins and Mitchell

(1997) [10]. The layer-by-layer approach goes by the means of numerical integration and

was performed based on the following assumptions:

1) Plane sections before bending remain plane and perpendicular to the neutral axis

after bending. This beam theory by Bernoulli allows linear strain distributions.

2) Strain in the steel and strain in the surrounding concrete is equaled due to the

perfect bonding between both types of materials. This behavior is valid prior to

the cracking of concrete and after yielding of steel reinforcement. In addition,

this assumption allows the concrete strain, at the level of reinforcement, to be

used in the analysis if the strain in steel was not properly captured.

3) Concrete is strong in compression but weak in tension, thus concrete tensile

strength is neglected after the initiation of the first crack.

4) The strains are uniform over the width of the section and the concrete section is

subjected to axial strains only.

Due to the amount of work necessary to predict the full flexural response, the analysis

procedure was carried out using available spreadsheet software. Determination of moment

and curvature prediction was performed according to the following steps:

1) A strain at the extreme compression fiber of the concrete, εc, is assumed.

2) A neutral axis depth, c, is assumed.

97

3) The internal forces in the compression and tension zones, as shown in

Equation 5.2, was determined based on the tensile strain at the level of

reinforcement using an iterative procedure.

T + C = 0 Eqn. 5.2

where,

T = internal forces in tension zones which consist of the tension force

from concrete, Tc, and the tension force from the tension

reinforcement, Ts.

C = internal forces in compression zones which consist of the

compression force from concrete, Cc, and the compression force from

the compression reinforcement, Cs.

4) The section equilibrium was checked according to Equation 5.3.

∫ ∫ ∫ ∫ =+++ 0''' cctAcssAsssAscAc dAfdAfdAfdAcf Eqn. 5.3

where,

fc = concrete stress in compression

fs’ = steel stress in compression

fs = steel stress in tension

fct = concrete stress in tension

Ac = area of concrete

As’= area of compression steel reinforcement

As = area of tension steel reinforcement

98

5) The assumed value of neutral axis depth, c, was revised until section

equilibrium was achieved.

6) The internal moment of the section, Mn, was determined by the summing of

the internal force respected to the neutral axis of the section. The equation is

expressed in Equation 5.4.

∫ ∫ ∫ ∫+++= cctAcssAsssAscAcn ydAfydAfydAfydAcfM ''' Eqn. 5.4

where,

y = a distance measured from the neutral axis to the corresponding

force

Mn = Nominal or resisting moment

7) The applied load, P, is derived directly from the bending moment, Mn.

8) The curvature relationship is calculated based on Bernoulli’s beam theory, as

expressed on Equation 5.5. The tension force in concrete is neglected after

the initiation of the first crack.

ccε=Φ Eqn. 5.5

where,

Φ = curvature at a given strain increment

εc = concrete strain at the extreme compression fibers

c = neutral axis depth taken at the extreme compression

fiber

99

9) The concrete strain in the extreme compression fiber is increased and steps 2

to 8 are repeated.

10) The analytical model for moment and curvature relationship is terminated as

the concrete strain, εc, reaches the crushing value of 0.0038 in/in.

5.6.1 Cracking Moment Calculation

Cracking moment, Mcr, is calculated based on Equation 5.6.

yt

fIM rg

cr = Eqn. 5.6

where,

Mcr = cracking moment

fr = modulus of rupture of concrete

Ig = gross moment of inertia

yt = neutral axis depth from tension side

5.6.2 Failure Criteria

All specimens were designed to comply with the new ACI “Unified Method.” In

order to do so, each net tensile strain in the reinforcement, εt, must be equal to or greater than

0.005 in/in at failure. In addition, each specimen was also checked to avoid premature failure

due to shear. The “Unified Method” was performed for each beam to ensure a fully tension-

controlled and ductile failure. This type of failure is favorable in structural concrete

members due to the ample warning effect of large deflections and extensive cracking prior to

100

the crushing of the concrete. Compression failure occurred by the crushing of the concrete

when the extreme compression fiber in the beam reached the ultimate strain value while the

strains in the reinforcements were elastic.

5.7 MATERIAL MODELING

The four materials used in this project consisted of normal weight concrete, #4 and #6

A615 Grade 60 steel, and #6 MMFX steel. Modeling of each material was based on the

experimental measurements from testing and the analytical models based on published

literature. The measured strength values are reported at the beginning of Chapter 4.

5.7.1 Concrete

The stress-strain relationship of the concrete was modeled based on Hognestad

concrete stress-strain relationship, as seen in Figure 5.13. The concrete strain corresponding

to the maximum stress, εo, was calculated based on Equation 5.7, which documented in Park

and Pauley [21].

oε =c

c

Ef ''2

Eqn. 5.7

where,

f″c = concrete stress corresponding to eighty-five percent of

the compressive strength at the time of testing

f′c = compressive strength at the time of testing

Ec = modulus of concrete = cf '57000

101

The maximum strain in concrete, εcu, is 0.0038 in/in at the corresponding concrete

stress of 72.25 percent of maximum compressive strength. The rising portion of the stress-

strain curve is portrayed by a parabolic equation, which is displayed in Equation 5.8. The

descending portion is determined from a linear equation.

−=

22

''o

c

o

ccc ff

εε

εε

Eqn. 5.8

where,

fc = compressive strength calculated from concrete strain at any

given value below εo.

f″c = 0.85f’c

εo = strain in concrete corresponding to the maximum stress.

εc = compressive strain in concrete at any given value below εo.

The rupture strength of concrete was calculated according to ACI 9.5.2.3.

cr ff '5.7= Eqn. 5.9

5.7.2 Compression Reinforcement

A615 Grade 60 compression rebar was modeled to be perfectly plastic. The yield

strength of 62.67 ksi at yield strain of 0.00243 in/in was averaged from tension tests. For

modeling purpose, the elastic modulus of 29000 ksi was used. The stress-strain curve of the

#4 bar is displayed in Figure 5.14.

102

5.7.3 Tension Reinforcement

Tension reinforcement consisted of A615 Grade 60 steel on Beam B1, and MMFX

steel on the remaining three beams (Beam B2, B3, and B4).

A stress-strain relationship for mild carbon steel is assumed to be elastic up to the

yield stress of 63.54 ksi at the yield strain of 0.00223 in/in. An elastic modulus value of

29000 ksi was used for the modeling. The strain hardening was modeled to have low rate of

change, based on the yielding strength and ultimate strength of the rebar at failure.

The tensile properties of the MMFX rebar in Beam B2, B3, and B4 was modeled

from Equation 5.10. This equation was modified from the original equation through the

process of trial and error in order to match the actual strength values in tension tests.

( )sef sε1851177 −−= Eqn. 5.10

where,

fs = tensile stress in the MMFX rebar

εs = tensile strain in the MMFX rebar

It is important to report that the modulus of elasticity of the MMFX rebar is slightly

lower than that of the Grade 60 steel. Due to very small difference between the moduli, it is

safe to use the modulus of elasticity of the MMFX as 29000ksi.

103

Stress-strain curves of the compression and tension reinforcement is illustrated in

Figure 5.5.

5.8 DEFLECTION PREDICTION [10]

The midspan deflection for each beam was determined from the integration of the

curvature along the beam. The corresponding curvature at each loading increment was

obtained from the result of moment-curvature analysis presented in Figure 5.16. The

deflection prediction was performed numerically from the support to the midspan section.

This procedure gives the maximum deflection at each specified load level. For this project,

the numerical integration was performed for 10 sections along the half of the span, 2L ,

according to Equation 5.11. It should be noted that the moment-curvature relationship used

for deflection calculation did not account for tension stiffening.

∑ ∆

Φ+Φ

=∆ ++i

iiii xxx

211 Eqn.5.11

where,

∆ = deflection

ix = distance from the origin to ix

iΦ = curvature corresponding to ix

1+Φ i = curvature corresponding to 1+ix

1+ix = distance from the origin to 1+ix

ix∆ = change in distance between 1+ix - ix

104

The numerical integration of the curvature for deflection calculation for a simply

supported beam is illustrated in Figure 5.17. The theoretical deflection in each beam is

compared with the experimental deflection in the next section.

5.9 VERIFICATION OF ANALYTICAL MODEL

In order to verify the analytical model, theoretical load-midspan deflection curves,

derived from the integration of curvature, was compared with the actual test values. The

verification process was performed only in Beam B1, Beam B2, and Beam B3. The

verification process consisted of two sections: 1) Grade 60 Beam, and 2) MMFX Beams

5.9.1 Grade 60 Beam

As seen in Figure 5.18, the predicted load and deflection behavior of the Grade 60

reinforcing beam, Beam B1, has an excellent correlation with the experimental result in

terms of cracking load, stiffness, yielding load, and ultimate load. The theoretical prediction

was very close to the measured data obtained from the experiment. The predicted deflection

at the service load of 19.38 kips (0.6fy) was 0.38 inch. The measured experimental service

load was 20.5 kip. The difference between the predicted and measured values is within an

acceptable range. The experimental and theoretical deflection at service load was lower than

the permissible deflection calculated at 360L . The results indicated that the theoretical model

was valid and the beam functions satisfactorily under the service condition.

105

5.9.2 MMFX Beams

Similar findings from Beam B1 were observed in Beam B2. The correlation between

the measured and the predicted results was nearly indistinguishable from cracking of up to 70

percent of the maximum capacity. Slightly higher stiffness value led to a slight over-

estimation of the failure load. The predicted deflection at ultimate is the same at 3.1 inches

at the crushing strain of 0.003 in/in for Beam B2. The ultimate load calculated from the

analytical model at the crushing concrete strain of 0.003 in/in proves to be slightly higher at

58 kips in comparison to the 55.8 kips in actual data as shown in Figure 5.19. The difference

is accountable to the loading condition and the material modeling of concrete. The

theoretical and experimental service load deflection showed very good agreement with less

than 5 percent difference.

As evident from Figure 5.19, Beam B3’s theoretical load-midspan deflection had an

excellent correlation of up to 80 percent of the ultimate load. The predicted deflection at the

concrete crushing strain of 0.003 in/in is 2.5 inches, which is nearly the same as the measured

deflection of 2.6 inches. The ultimate load calculated from the analytical model was 8

percent higher than the measured ultimate load of 77.8 kips. The theoretical deflection at

service load showed good agreement with the experimental value.

It should be noted that the deflection at service load for the MMFX beams were

determined from the mid-span deflection corresponding to 48-ksi stress (0.6fy) in the MMFX

rebars.

106

The results prove that the analytical model for the MMFX beams were very effective,

with a minor exception on higher prediction of the ultimate strength.

5.10 MODIFIED MMFX MODEL

As mentioned earlier, the maximum yield strength specified by ACI for deformed

reinforcement allowed for reinforced concrete structure was 80 ksi (ACI 9.4). In order to

comply with this regulation, the MMFX stress-strain behavior was modified to comply with

the 80-ksi maximum yield strength.

In order to study the effect of the modified strength and stress-strain curve of the

MMFX steel rebar, the analytical model was carried out using the design parameters of Beam

B3 reinforced with MMFX with the reinforcement ratio of 0.0074. The adopted materials

model is Hognestad stress-strain curve for concrete and the perfectly elastic stress-strain

curve for compression steel with the elastic modulus of 29000 ksi. The modified MMFX

model for tension reinforcement is described in Equation 5.12.

for 0 < εs < 0.00325 in/in

)1(177 185 sef sε−−= ksi

for εs > 0.00325 in/in Eqn 5.12

sf = 80 ksi

Figure 5.20 shows the actual MMFX stress-strain curve modified to the 80-ksi yield

stress level limit. It is important to indicate that the modification neglected the high-strength

properties of the original MMFX steel.

5.10.1 Response of Beams Based on the Modified MMFX Characteristics

107

The response of Beam B3, according to the modified MMFX model, is shown in

Figure 5.21. The analysis followed the procedure described in section 5.7 and section 5.8.

The load-midspan deflection of the modified MMFX steel followed the prediction by

using the actual model up to the yield stress of 80 ksi at the loading of 42 kip. This finding

indicated that the deflection of the beam, designed using the modified MMFX, was slightly

conservative in comparison to the actual MMFX model behavior.

The results from using the modified model suggested excellent agreement of load-

midspan deflection behavior up to the yield strength. However, the modified MMFX model

underestimated the ultimate load capacity by 40 percent. The ultimate deflection was 0.5 inch

higher at the concrete strain of 0.003 in/in. The deflection corresponding to concrete strain

of 0.0038 in/in was 4.12 in/in. Therefore, beams designed using the modified MMFX are

very conservative.

5.11 Parametric Study

The objective of this section is to establish a design guideline in terms of net tensile

strain (εt), and the reinforcement ratio (ρ) for flexural rectangular concrete members

reinforced with MMFX rebar. According to ACI, tension-controlled failure occurred when

the net tensile strain in the extreme tension steel at failure is greater or equal to a steel strain

of 0.005 in/in when the concrete compression stain reaches 0.003 in/in. This type of failure

is preferred, due to the ample warning displayed through excessive crack and large

deformation prior to failure, in order to avoid a sudden compression-controlled failure. All

tension-controlled sections are subjected to the reduction factor, φ , of 0.9. Due to little

108

warning of a brittle failure in compression-controlled sections, the reduction factors were

taken at 0.65 when the net tensile strain in the extreme tension steel is less than or equal to

0.002 in/in at the failure. A section with net tensile strain between 0.002 in/in to 0.005 in/in

at a corresponding concrete compression strain of 0.003 in/in is described as being in a

transition zone. The reduction factor for the transition zone member is determined from

Equation 5.13.

φ = 0.48+83 εt Eqn. 5.13

where,

φ = reduction factor for flexural member

εt = net tensile strain in the extreme tension steel

This analysis was based on material characteristics that consisted of a perfectly

elastic-plastic model for mild steel, actual MMFX, and a modified MMFX model. To

simplify the analysis, the compression steel and tension force in concrete were ignored. The

rectangular concrete section used is 12 inches wide by 18 inches high. The εt-ρ analysis was

performed for concrete compression strength ranges of 4000, 7000, and 10000 ksi. Depth of

the equivalent stress block was based on ACI 318-02 clause 10.2.7.3.

The analysis was carried out using a standard procedure found on ACI stress block

theory. The analysis was performed iteratively by changing of neutral axis depth, c, while

maintaining the section equilibrium. The maximum compressive strain at the crushing of the

concrete, εc, was taken conservatively at 0.003 in/in.

109

5.11.1 Results and Discussion of Parametric Study

The results from the analysis were presented based on the relationship between the

maximum tensile strain (net tensile strain) of the reinforcement at failure, εsu, and the

reinforcement ratio, ρ, in Figure 5.22 through Figure 5.27. Reinforcement ratio versus the

ultimate strain of the steel, εsu-ρ, using concrete strength of 4000 psi, 7000 psi, and 10000

psi, are presented in Figure 5.22, 5.23, and 5.24 respectively. In each figure, the maximum

tensile strains of the reinforcement at failure corresponding to minimum reinforcement ratio,

minimum ductility at strain of 0.005 in/in, maximum reinforcement ratio at strain of 0.004

in/in, and balanced reinforcement condition are shown. The minimum, recommended

maximum (minimum ductility), maximum, and balanced conditions are respectively denoted

by solid rectangular, diamond, triangle, and circle shapes. The minimum reinforcement ratio

for each concrete class was calculated based on y

c

ff '3

, where the yield stress was 60 ksi for

A615 Grade 60 steel, and 80 ksi for MMFX steel. The recommended maximum and

maximum reinforcement were determined at the maximum tensile strain of the reinforcement

of 0.005 in/in, and 0.004 in/in respectively. The balanced reinforcement was calculated

based on the yielding strain of the reinforcements, εy is 0.002 in/in for mild steel, assumed

yield strain of 0.00325 in/in for MMFX at stress equal to 80 ksi, and the crushing concrete

strain in concrete is 0.003 in/in. The range for the concrete section to behave in tension-

controlled manner, maximum design range, occurs between the maximum and minimum

reinforcement, which is indicated by a dashed line. Similarly, the recommend range for the

110

section to meet the ACI minimum ductility requirement, recommend maximum design range,

begins at minimum and ends at the recommended maximum reinforcement, which is also

shown by dashed line. The summary of the findings is presented in Table 5.2. The values

are reported in terms of ultimate strain in steel (εsu), ultimate stress in steel (fsu), normalized

nominal moment ( 2' bdfM

c

n ), normalized ultimate moment ( 2' bdfM

c

nφ) corresponding to

minimum, recommend maximum (minimum ductility), maximum, and balanced

reinforcement condition for each concrete strength, and material modeling.

The observed behavior of the εsu-ρ relationship from Figure 5.22 to 5.27 indicates that

concrete sections follow the typical relationship of reinforced concrete members, regardless

of the type of reinforcements. In general, reinforced concrete sections with lower

reinforcement ratios behave in a more ductile manner in comparison to a higher reinforced

section. This common behavior is displayed through out εsu-ρ curves seen in Figure 5.22 to

Figure 5.27. Since similar behavior occurred throughout all concrete strengths, the only

results that need to be discussed in detail are the results obtained from the 7000 psi concrete

class.

In Figure 5.23, concrete section design based on the actual MMFX model displayed a

lower amount of section ductility in comparison to a concrete designed section based on

conventional steel model. This behavior is true for any MMFX reinforcing sections whose

reinforced ratios are less than the balanced reinforcement of the Grade 60 steel model. In

order to benefit from the high-strength property of the MMFX rebar, MMFX reinforced

111

sections should be designed between the reinforcement ratios of 0.31 to 4.31 percent. At this

design range, the actual steel stress of the MMFX rebars at failure can vary from 60 ksi to

170 ksi, while the straining of the MMFX rebar can reached up to 0.02 in/in.

At a typical design range (0.5ρb to 0.6ρb) of 1.5 percent, the designed section based

on the actual MMFX model and 7000 psi concrete strength, is capable of a 70 percent

increase in section capacity in comparison to the conventional steel model, as shown in the

2' bdfM

c

n -ρ curves illustrated in Figure 5.29. In addition, up to 70 percent of the steel can be

saved by making a switch from Grade 60 steel to a high-strength MMFX steel rebar. For

7000 ksi concrete, a recommend range for a section to have tension-controlled failure, and to

satisfy the ACI minimum ductility requirement, was taken at a reinforcement ratio of 0.31 to

1.46 percent, which is narrower than the range for Grade 60 steel model. The ultimate steel

stress between 67.0 ksi to 174.9 ksi corresponding to a recommended maximum design

range, indicates that the high-strength properties of the MMFX steel are fully utilized.

It is important to report that the behavior of the designed concrete section based on

the modified elastic-plastic relationship of the stress-strain of MMFX steel was slightly more

ductile in behavior than the designed section based on the actual MMFX steel. This behavior

leads to a more conservative prediction of the ultimate moment. These findings are true for

any modified MMFX section, whose reinforcement ratio is less than that of the actual

MMFX model’s balanced reinforcement condition. The modified MMFX model provides

wider range for reinforcement ratio, 0.31 to 1.95 percent, in contrast to the range of 0.031 to

112

1.46 percent of reinforced steel ratio using the actual stress-strain model. A 20 percent

decrease in predicted section capacity of the modified MMFX at a typical design range of 1.5

percent confirms a safe and more conservative design approach to reinforced concrete

structures with MMFX steel reinforcement.

MMFX steel functions more adequately in higher concrete strength structures. This

conclusion was drawn from a wider design range for a concrete section to behave in tension-

controlled failure, a more ductile behavior, and stronger section capacity of the reinforced

concrete sections with MMFX reinforcement of 10000 psi in contrast to a concrete strength

of 4000 psi. This behavior is illustrated in Figure 5.25 to 5.27, for sections designed using

the Grade 60 steel, actual MMFX, and modified MMFX steel model. Figure 5.31, 5.32, and

5.33 shows relationship between reinforcement ratio, ρ, and normalized ultimate

moment, 2' bdfM

c

nφ, where the reduction factor, φ, was applied to

2' bdfM

c

n -ρ relationship in

Figure 5.28, 5.29, and 5.30.

113

Table 5.1: Summary of test results

Beam B1 Beam B2 Beam B3 Beam B4 (static loading) (static loading) (static loading) (slow cyclic loading)

Tension Reinforcement 3 # 6 2 # 6 3 # 6 3 # 6 Compression Reinforcement 2 # 4 2 # 4 2 # 4 2 # 4

As (in2) 1.32 0.88 1.32 1.32 As' (in2) 0.4 0.4 0.4 0.4

Reinforcement Ratio 0.00704 0.00469 0.00704 0.00704 Tension steel Grade 60 Steel MMFX Steel MMFX Steel MMFX Steel

Compression steel Grade 60 Steel Grade 60 Steel Grade 60 Steel Grade 60 Steel Cracking Load (kip) 8.5 8 10 10

Service Load (fsl = 0.6fy) 20.5 18 21.4 21.4 29.87 @ 80ksi 42.57 @ 80ksi 40.57 @ 80ksi

Yielding Load (kip) 33 45.21@ 120ksi 66.8@ 120ksi 56.43 @ 120ksi Ultimate Load (kip) 40.7 54.7 77.9 72.6

Unloading Load (kip) N.A. 50 74.2 69.1 Gross Stiffness (kip/in) 168.6 165.4 167.3 169.2

Deflection @ service load (in) 0.36 0.44 0.35 0.38 0.84 @ 80ksi 0.86 @ 80ksi 0.8 @80ksi

Deflection @ yield (in) 0.7 1.71@ 120ksi 1.76 @ 120ksi 1.32 @ 120ksi Deflection @ Ultimate Load (in) 3.87 3.1 2.7 2.29

Deflection @ Unloading (in) 3.87 4.06 2.95 3.29 Steel strain @ ultimate 0.0201 0.00983 0.00912 0.0095 Steel strain @ unload 0.0201 0.0179 0.0129 0.02017

Steel stress @ ultimate 73.5 146.3 140.02 141.97 Steel stress @ unload 73.5 164.88 154.47 167.78

Concrete strain @ ultimate 0.00427 0.0029 0.0032 0.00698 Crack width @ service load 0.0138 0.019 0.0135 0.0135

Maximum crack width 0.19 0.12 0.085 0.06 Total number of crack 16 23 32 32

Failure Mode Crushing of Concrete Crushing of Concrete Crushing of Concrete Crushing of ConcreteLocation of Failure Right Load Right Load Left Load Right Load

Severity Level of Failure Medium High Medium Medium

114

Table 5.2: Summary of parametric study f'c=10000 psi f'c=7000 psi f'c=4000 psi

Mn φ Mn Mn φ Mn Mn φ Mn

MMFX ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 F'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ min,Fy=80ksi 0.38 0.063 0.056 0.0224 174.18 0.31 0.074 0.066 0.0201 172.68 0.24 0.096 0.087 0.0184 171.08

ρ ductility 1.94 0.180 0.161 0.0050 106.81 1.46 0.194 0.173 0.0050 106.81 1.01 0.235 0.212 0.0050 106.81 ρ max 2.56 0.201 0.163 0.0040 92.55 1.93 0.217 0.176 0.0040 92.55 1.34 0.263 0.214 0.0040 92.55

ρb,Fy=80ksi 3.31 0.221 0.165 0.00325 80.00 2.50 0.238 0.178 0.00325 80.00 1.73 0.289 0.216 0.00325 80.00 ρ ductility- ρ min 1.56 0.117 0.105 0.0174 67.37 1.15 0.120 0.107 0.0151 65.86 0.78 0.139 0.125 0.0134 64.27 ρ max- ρ min 2.18 0.139 0.107 0.0184 81.63 1.61 0.143 0.110 0.0161 80.12 1.10 0.167 0.127 0.0144 78.53


Modified MMFX ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 F'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ min,Fy=80ksi 0.38 0.029 0.026 0.0523 80.00 0.31 0.035 0.032 0.0468 80.00 0.24 0.046 0.042 0.0427 80.00

ρ ductility 2.59 0.180 0.161 0.0050 80.00 1.95 0.194 0.173 0.0050 80.00 1.35 0.235 0.211 0.0050 80.00 ρ max 2.96 0.201 0.163 0.0040 80.00 2.23 0.217 0.176 0.0040 80.00 1.55 0.263 0.214 0.0040 80.00



Grade60(Fy=58ksi) ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 F'cbd2 εsu (in/in) fsu (ksi) ρ (%) f'cbd2 f'cbd2 εsu (in/in) fsu (ksi) ρ min,Fy=58ksi 0.50 0.028 0.026 0.0542 58.00 0.42 0.034 0.031 0.0485 58.00 0.32 0.045 0.04 0.0443 58.00

ρ ductility 3.57 0.180 0.161 0.0050 58.00 2.69 0.194 0.173 0.0050 58.00 1.87 0.235 0.211 0.0050 58.00 ρ max 4.08 0.201 0.163 0.0040 58.00 3.08 0.217 0.176 0.0040 58.00 2.14 0.263 0.214 0.0040 58.00


115

Figure 5.1: Load-midspan deflection relationship for Beam B1 and Beam B3

Figure 5.2: Load-steel strain relationship for Beam B1 and Beam B3

Beam B1

Beam B3

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5


Load

(kip

)

Beam B1

Beam B3

0

10

20

30

40

50

60

70

80

90

0.000 0.005 0.010 0.015 0.020 0.025Steel Strain (in/in)

Load

(kip

)

116



Beam B2

Beam B3

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Midspan Deflection (in)

Load

(kip

)

Beam B2

Beam B3

0

10

20

30

40

50

60

70

80

90

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020


Load

(kip

)

117



Beam B4Beam B3

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Midspan Deflection (in)

Load

(kip

)

Beam B3

Beam B4

0

10

20

30

40

50

60

70

80

90

0.000 0.005 0.010 0.015 0.020 0.025


Load

(kip

)

118

Beam B1

Beam B2

Beam B3

Beam B4

Figure 5.7: Pattern of crack for all beams

, Ill."

\' ,

" ,

• .,

'. "1:8 \ i..\~. \9/t'

119

Figure 5.8: Load-crack width relationship for all beams

Figure 5.9: Load-concrete strain for all beams

Beam B1

Beam B2

Beam B3

ACI: 0.016"

Beam B4

0

10

20

30

40

50

60

70

80

90

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Crack Width (in)

Load

(kip

)

Beam B1Beam B1

Beam B2Beam B2

Beam B3

Beam B3Beam B4

Beam B4

minimum ductility

0.0030

10

20

30

40

50

60

70

80

90

-0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025


Load

(kip

)

concrete strain @ level of bottom steelConcrete strain @ top surface

120

Beam B1

Beam B2

Beam B3

Beam B4

Figure 5.10: Failure mode for all beams

121

Figure 5.11: Load-midspan deflection at service load for beams tested under static conditions

Figure 5.12: Load-crack width at service load for beams tested under static conditions

Beam B1

Beam B2

Beam B3

l/360 = 0.5"

0

10

20

30

40

50

60

70

80

90

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5


Load

(kip

)

Beam B1

Beam B2

Beam B3

ACI: 0.016"

0

10

20

30

40

50

60

70

80

90

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Crack Width (in)

Load

(kip

)

122

Figure 5.13: Stress-strain model for concrete

Figure 5.14: Stress-strain model for compression reinforcement

Figure 5:15: Stress-strain models for tension reinforcements

ε co

f'' c = 0.85f' c

f c =0.85f'' c

ε cu0

1000

2000

3000

4000

5000

6000

7000

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004Concrete Strain (in/in)

Con

cret

e St

ress

(psi

)

E s = 29000 ksi

Grade 60

0

10

20

30

40

50

60

70

0 0.005 0.01 0.015 0.02 0.025 0.03Steel Strain (in/in)

Stee

l Str

ess

(ksi

)

MMFX

Grade 60E sh = 515 ksi

E s = 29000ksi

0

20

40

60

80

100

120

140

160

180

200

0 0.005 0.01 0.015 0.02 0.025 0.03Strain (in/in)

Stre

ss (k

si)

123

Figure 5.16: Moment-curvature and Moment-steel strain relationship for beams tested under

static conditions

B3: Experimental

B3: Theoretical

B2: Experimental

B2: Theoretical

B1: Experimental

B1: Theoretical

0

500

1000

1500

2000

2500

3000

3500

0 0.0005 0.001 0.0015 0.002 0.0025

Curvature (rad/in)

Mom

ent (

kip-

in)

B1: Theoretical

B1: Experimental

B2: Theoretical

B2: Experimental

B3: Theoretical

B3: Experimental

0

500

1000

1500

2000

2500

3000

3500

0 0.005 0.01 0.015 0.02 0.025 0.03


Mom

ent (

kip-

in)

124

Figure 5.17: Deflection calculation

125

Figure 5.18: Theoretical and experimental load-midspan deflection for Beam B1

Figure 5.19: Theoretical and experimental load-midspan deflection for Beam B2 and Beam

B3

20.45K

0.36"

ACI

0.50"

4.33"@0.0038

3.46"@0.003

0

5

10

15

20

25

30

35

40

45

50

0.0 1.0 2.0 3.0 4.0 5.0

Midspan Deflection (inch)

Load

(kip

)

2.58" @ 0.0031

22.6 K

0.5"

ACI

Beam B3

2.5"@0.003"

3.05"@0.0038"

3.08" @ 0.0029"Beam B2

3.89"@0.0038

3.13"@0.003

17.0K

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Midspan Deflection (inch)

Load

(kip

)

126

Figure 5.20: Stress-strain model for Modified MMX steel

Figure 5.21: Theoretical and experimental load-midspan deflection for Beam B3

2.58" @ 0.0031in/in

22.6K

0.5"

ACI

Beam B3

2.5"@0.003in/in

3.05"@0.0038in/in

3.18"@0.003in/in 4.12"

@0.0038in/in

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5Midspan Deflection (inch)

Load

(kip

)MMFX

Modified MMFX

0

20

40

60

80

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1 0.12

Strain (in/in)

Stre

ss (k

si)

127

Figure 5.22: Ultimate steel strain-reinforcement ratio for 4000 psi concrete

MMFX

Grade 60

Modified MMFX

0.0020.004

0.0184

0.0427

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 1 2 3 4 5 6

Reinforcement ratio (%)

Ulti

mat

e st

eel s

trai

n (in

/in)

= mininimum reinforcement ratio

= minimum ductility at steel strain = 0.005 in/in

= maximum reinforcement ratio at steel strain = 0.004 in/in

= balanced reinforcement ratio

128


MMFX1.

46

B2

B3

Gra

de 6

0

0.31

1.93

Mod

ified

MM

FX

0.42 2.7

B1

0.0020.0040.005

0.0468

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5 6


Ulti

mat

e st

eel s

trai

n (in

/in)





129


MMFX

MMFXModified

Grade 60

0.0020.0040.005

0.0224

0.0523

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5 6


Ulti

mat

e st

eel s

trai

n (in

/in) = mininimum reinforcement ratio




130

Figure 5.25: Ultimate steel strain-reinforcement ratio for Grade 60 steel model

f'c=7ksi

f'c=10ksi

f'c=4ksi

0.0020.0040.005

0.0541

0.0485

0.0443

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5 6


Ulti

mat

e st

eel s

trai

n (in

/in)





131

Figure 5.26: Ultimate steel strain-reinforcement ratio for actual MMFX model

f'c=10ksi

f'c=7ksi

f'c=4ksi

0.004

0.0224

0.0201

0.0184

0.00325

0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5 6


Ulti

mat

e st

eel s

trai

n (in

/in)





132

Figure 5.27: Ultimate steel strain-reinforcement ratio for modified MMFX model

f'c=10ksi

f'c=7ksi

f'c=4ksi

0.0020.0040.005

0.0523

0.0468

0.0427

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5 6


Ulti

mat

e st

eel s

trai

n (in

/in)





133

Figure 5.28: Normalized nominal moment-reinforcement ratio for 4000 psi concrete

2' bdfM

c

n

Grade60

Modified MMFX

MMFX

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4 5 6 7Reinforcement ratio (%)

Nom

aliz

ed N

omin

al M

omen

t





134


0.53

MMFX

Modified MMFX

Grade600.

31

1.45

Beam B2

Beam B3

2.5

0.42

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5 6 7


Nom

aliz

ed N

omin

al M

omen

t





2' bdfM

c

n

135


MMFX

Modified MMFX

Grade60

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35


Nor

mal

ized

nom

inal

Mom

ent





2' bdfM

c

n

136

Figure 5.31: Normalized ultimate moment-reinforcement ratio for 4000 psi concrete

MMFX

Modified MMFX

Grade60

0

0.05

0.1

0.15

0.2

0.25

0.3


Nom

aliz

ed U

ltim

ate

Mom

ent





2' bdfM

c

nφ

137


Grade60Modified MMFX

MMFX

Beam B2

Beam B3

0

0.05

0.1

0.15

0.2

0.25


Nom

aliz

ed U

ltim

ate

Mom

ent





2' bdfM

c

nφ

138


MMFX

Modified MMFX

Grade60

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2


Nor

mal

ized

Ulti

mat

e M

omen

t





2' bdfM

c

nφ

139

CHAPTER 6

SUMMARY AND CONCLUSIONS

6.1 SUMMARY

In this experimental program, four rectangular concrete beams with 12”x18”x15’

were tested to failure by a 440-kip capacity MTS actuator under stroke control conditions.

Three beams were reinforced with high-strength MMFX rebars and one beam was reinforced

with conventional Grade 60 steel rebars. The three beams were tested under static loading

conditions, while the last MMFX reinforced beam was tested under slow cyclic loading

conditions. The reinforcement for static beams consisted of 3 #6 A615 Grade 60 rebars, 2 #6

MMFX rebars, and 3 #6 MMFX rebars. The last beam was also reinforced with 3 #6 MMFX

rebars.

All beams were fully instrumented to monitor midspan deflection, concrete strain,

steel strain, and crack information, to study the flexural behavior of each beam from the

beginning to failure. The experimental results and analysis conducted in this research are

steered toward the development of design recommendation, which will address the use of

MMFX rebars as reinforcements for structural concrete applications.

6.2 CONCLUSIONS

Based on observed behavior, experimental results, theoretical prediction, and

additional analysis, the following conclusions were made:

140

1) Based on the results of tension tests, the stress-strain relationship of the

MMFX rebars can be modeled using an exponential equation. The exponential

model gives excellent correlation to the actual test results with an exception of

over-estimation beyond the 140-ksi stress level.

2) All beams reinforced with MMFX steel behaved non-linearly after the

initiation of the first crack and continued to behave in a similar manner up to

failure. This behavior is due to the non-linear nature of the MMFX material.

3) All MMFX beams function satisfactory up to failure. No premature failure

from bond or shear was observed in any beam. The failure mode was tension-

controlled failure.

4) All MMFX beams exhibit a very ductile flexural failure, which is common in

a beam with tension-controlled failure. The mode of failure was always

classified as a ductile flexural failure, which is evident from the significant

straining of reinforcement followed by concrete crushing in a compression

zone.

5) Prior to failure, MMFX beams provide adequate warning through large

deformation, and extensive cracking.

6) In comparison to a controlled beam, a 3 #6 MMFX beam exhibits similar

stiffness values before and after the initiation of the first crack in comparison

to a similar beam reinforced by Grade 60 steel. In addition, MMFX beams

have much higher ultimate strength and a comparable amount of ductility in

comparison to equally reinforced Grade 60 beams.

141

7) A lightly reinforced MMFX beam experienced more stiffness reduction, crack

growth, and deformation at the same load level as a highly reinforced MMFX

beam. A lightly reinforced section also produces a more ductile flexural

failure.

8) A beam reinforced with MMFX rebars functions satisfactory under a cyclic

loading condition. Typical behavior, such as deterioration of stiffness, more

straining of steel and concrete, and lower ultimate strength, were observed in

this beam.

9) All MMFX beams behave in a satisfactory manner under service load. All

deflections and crack widths determined at a 48 ksi stress level were below

the ACI allowable limits. It should be noted that the serviceability at a higher

stress level might exceed the permissible values.

10) Flexural behaviors of the MMFX beams can be modeled accurately by using

current available reinforced concrete theories.

11) The analytical model suggests that MMFX rebar is more efficient with higher

strength concrete.

12) The modified MMFX model shows good prediction at service load conditions.

However, it underestimates the ultimate strength of the section. This very

conservative model is suitable for a design application, but for a more

accurate prediction an analysis that features an actual stress-strain model must

be carried out to ensure confidence.

142

13) Increasing the applied load creates more cracks rather than widening existing

cracks. Therefore, the use of MMFX provides better crack control after the

yielding of reinforcement in comparison to Grade 60 steel.

6.3 RECOMMENDATIONS FOR FUTURE STUDY

In order to achieve an overall understanding of reinforced concrete beam flexural

behavior with MMFX rebars, future research should be continued in the following areas:

1) More tests must be performed to evaluate the consistency of MMFX steel as a

concrete reinforcing material.

2) A study of MMFX reinforcing steel on T and I-beams must be performed due

to the lack of documented literature on this topic.

3) A 2-million cycles fatigue test should be pursued in order to provide fatigue

strength results.

4) Future experimental programs on MMFX reinforcing beams subjected to

severe environmental conditions should be done to verify the highly

corrosion-resistant nature claimed by the manufacturer.

5) Future testing on over-reinforced, under-reinforced, and balanced-reinforced

concrete beams using MMFX as reinforcement should be conducted in order

to generate more data on this topic.

6) Various studies on related topics, such as shear and column should be carried

out to develop a complete guideline on the use of MMFX rebars as

reinforcements for structural concrete applications.

143

CHAPTER 7

REFERENCES

1. ACI Committee 318, 2002. “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02).” American Concrete Institute, Farmington Hills, Michigan. pp.

2. Ansley, H. M. “Investigation into the Structural Performance of MMFX

Reinforcing.” MMFX Steel Corporation: Technical Resources. August 13, 2002. <www.mmfxsteel.com/technical_resources/default.asp#documentation>.

3. ASTM A370-97-02: Standard Test Method and Definitions for Mechanical Testing of Steel Products

4. ASTM C-143-00: Standard Test Method for Slump of Hydraulic Concrete

5. ASTM C39-01: Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens

6. ASTM C496-96: Standard Test Method for Splitting Tensile Strength of Cylinder Specimens

7. ASTM E8-01: Standard Method of Tension Testing of Metallic Materials

8. Clarke, J.L. “Alternative Material for the Reinforcement and Presstressing of Concrete.” Blackie & Professional. Chapman & Hall, 1993, pp. 204.

9. Clemena, G.G., and Virmani, Y.P. “ Corrosion Protection: Concrete Bridge.”

Federal Highway Administration (FHWA). Retrieved July14, 2003. <www.tfhrc.gov/structur/corros/introset/htm>.

10. Collins, P.M., and Michell, D. Prestressed Concrete Structures. Response

Publications, Canada, 1997. pp. 169-185

144

11. El-Hacha, R., and Rizkalla, S.H. “Fundamental Material Properties of MMFX Steel Rebars.” North Carolina State University, NCSU-CFL Report No. 02-04. July 2002.

12. Galloway, J., Chajes, J. M. “Application of High-Performance Materials to Bridges Strength Evaluation of MMFX steel.” University of Delaware: NSF-REU 2002. August 8, 2002. <http://www.ce.udel.edu/cibre/reu/02reports/Galloway.doc>.

13. Malhas, A.F. “Preliminary Experimental Investigation of the Flexural Behavior

of the Flexural Behavior of Reinforced Concrete Beams using MMFX Steel.” MMFX Steel Corporation: Technical Resources. July 2002. <www.mmfxsteel.com/technical_resources/default.asp#documentation>.

14. Michaluk, C.R. “Flexural Behavior of One-Way Concrete Slabs Reinforced by Glass-Fibre Reinforced Plastic Bars.” MS Thesis, Dept. of Civil and Geological Engineering, University of Manitoba, Winnipeg, Manitoba, Canada. May 1996.

15. “MMFX Microcomposite Steel (MMFX2).” Division of Construction

Engineering and Management, Purdue University: Emerging Construction Technologies. Retrieved April 4, 2003. <www.new-technologies.org/ECT/Civil/mmfx.htm>.

16. MMFX Steel Product Bulletin (February 2002)

<http://www.mmfxsteel.com/PDF/PRODUCT%20BULLETIN%20FEBRUARY%202002.pdf>

17. Pyc, A.W., Weyers, E.R., and Zemajtis, J. “Final Report: Field Performance of

Epoxy-Coated Reinforcing Steel in Virginia Bridge Deck.” Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, VTRC 00-R16. February 2000.

18. Park R., and Pauly T. Reinforced Concrete Structures. John Wiley and Sons,

1975.

19. Tullman Consulting. “Cost Related to Corrosion.” Corrosion-Club.com. Retrieved July 14, 2003. < www.corrosion-club.com/concretecosts.htm>.

20. Vijay, P.V., Gangarao, V.S. H, and Prachasaree, W. “Bending Behavior of

Concrete Beams Reinforced with MMFX Steel Bars.” MMFX Steel Corporation: Technical Resources. July 2002. <www.mmfxsteel.com/technical_resources/default.asp#documentation>.

145

21. Virmani, Y. P. “Corrosion Costs and Preventive Strategies in the United States.” U.S. Department of Transportation: Federal Highway Administration (FHWA), Office of Infrastructure Research and Development, Report FHWA-RD-01-156. September 2001.

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