EXPERIMENTAL INVESTIGATION ON MECHANICAL CHARACTERIZATION
OF FIBER REINFORCED FOAMED CONCRETE
A Thesis
Presented to
The Graduate Faculty of The University of Akron
In Partial Fulfillment
of the Requirements for the Degree
Master of Science
Mohammed Imtiaz Khan
May, 2014
EXPERIMENTAL INVESTIGATION ON MECHANICAL CHARACTERIZATION
OF FIBER REINFORCED FOAMED CONCRETE
Mohammed Imtiaz Khan
Thesis
Approved: Accepted:
______Advisor Department Chair Dr. Anil K. Patnaik Dr. Wieslaw K. Binienda
______Committee Member Dean of College Dr. Craig Menzemer Dr. George K. Haritos
______Committee Member Dean of the Graduate School Dr. Ping Yi Dr. George R. Newkome
______Date
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ABSTRACT
With the increase in demand for structures which are light in weight, researcher and industrialist interest in foamed concrete to be used in structural applications is steadily increasing. Foamed concrete is currently believed to have a promising future.
Foamed concrete was restricted to use as partition wall, thermal insulation, filling the void and rehabilitation work in the past. In the last two decades, with the understanding of the phenomenon underlying foamed concrete, researchers have studied various parameters that affects the performance of foamed concrete with and without fibers, and efforts have been made to use foamed concrete in structural application. The main objective of the research is to investigate the mechanical and structural properties of plain and fiber reinforced foamed concrete.
Foamed concrete also known as cellular concrete or lightweight concrete is a type of concrete with cementitious paste, fines, water and voids without coarse aggregate. The voids are created by using foam. The use of admixtures such as fly ash, silica fume and fibers in the foam concrete provide more strength than plain foamed concrete (PFC).
Under this research program, three different mixes were made: plain foamed concrete
(PFC), polypropylene fiber reinforced foamed concrete (PPFC) and basalt fiber reinforced foamed concrete (BFC). Specimens were tested for compressive strength, splitting tensile strength, young’s modulus and poisson’s ratio, flexural strength and RFC
(Reinforced foamed concrete) strength. This study showed that the use of optimum foam
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volume i.e. 20% gives a specific density of foam concrete 70 – 100 pcf and compressive strength of 3000 – 5500 psi. For the study of flexural application, eight different steel reinforced sandwich beams were tested. For study of compression application, sixteen compression columns, eight of them with reinforcement and eight without reinforcement were tested. Steel reinforced sandwich beams were divided into four different sets, two of each, normal concrete - Styrofoam R-13 rating combination, normal concrete - PFC combination, normal concrete - PPFC combination and normal concrete – BFC combination. Similarly, to study the structural behavior of the compression column, specimens were divided into different groups as that of sandwich beams. The flexural strength of BFC specimen was 10 times more than PFC specimen. Among the RFC beam specimens, BFC has shown maximum load carrying capacity. Also, experimental results show that normal concrete – BFC combination has shown the highest load carrying capacity under bending. Among the compression column normal concrete – PFC combination has shown the highest load carrying capacity.
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ACKNOWLEDGEMENTS
I would like to express my deepest gratitude to my advisor, Dr. Anil K. Patnaik for his excellence guidance throughout my graduate studies. The experience I have gained while working under his guidance has been exceptional, and I am grateful for his patience, continuous support and enthusiasm at all the time in my research.
I am also very thankful to my committee members, Dr. Craig Menzemer and Dr.
Ping Yi for their invaluable suggestions and insightful comments.
I would also like to acknowledge Sika Corporation US and Associated Ready Mix
Concrete for providing me the materials throughout my research. Also, I would like to extend sincere thanks to Mr. David McVaney and Mr. Brett Bell for their help in the laboratory. Very special thanks to my colleagues; Abdisa M. Musa, Sudeep Adhikari,
Mohammed Hafeez, Sunil Gowda, Mohamed Habouh, Sai K. Ganapuram, Srikanth
Marchetty and Prince Baah for helping me in casting and testing concrete specimens.
Finally, I would like to thank my family and friends for their continuous encouragement and support.
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TABLE OF CONTENTS Page LIST OF TABLES ...... x
LIST OF FIGURES ...... xii
LIST OF SYMBOLS ...... xviii
CHAPTER
I. INTRODUCTION ...... 1
1.1 Background ...... 1
1.2 Research Significance ...... 2
1.3 Research Objectives ...... 3
1.4 Scope of Thesis ...... 4
II. LITERATURE REVIEW ...... 5
2.1 Background and Introduction ...... 5
2.2 Comparison of foamed concrete and plain concrete ...... 6
2.3 Application ...... 7
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2.4 Materials ...... 11
2.5 Fiber ...... 13
2.6 Compressive Strength ...... 14
2.7 Splitting Tensile Strength ...... 18
2.8 Flexural Strength ...... 23
2.9 Modulus of Elasticity and Poisson’s Ratio ...... 27
2.10 Reinforced Foamed Concrete Beam and Sandwich Specimens ...... 31
III. EXPERIMENTAL PROGRAM ...... 42
3.1 Introduction ...... 42
3.2 Ingredients of Foamed Concrete ...... 42
3.2.1 Cement ...... 43
3.2.3 Silica Fume ...... 43
3.2.3 Foam ...... 44
3.2.4 Fiber ...... 46
3.2.5 Water ...... 46
3.3 Mix Design...... 47
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3.3.1 Mix Proportion ...... 47
3.3.2 Mixing Procedure ...... 47
3.3.3 Casting and Demolding ...... 48
3.4 Specimens Preparation and Testing Procedures ...... 49
3.4.1 Compression Tests ...... 49
3.4.2 Modulus of Elasticity and Poisson’s Ratio Test ...... 50
3.4.3 Splitting Tensile Test ...... 53
3.4.4 Flexural Beam Test ...... 54
3.4.5 Reinforced Foamed Concrete Beam Tests ...... 56
3.4.6 Sandwich Beam and Compression Column Tests ...... 57
IV. RESULTS AND DISCUSSION ...... 66
4.1 Compressive Strength ...... 66
4.2 Splitting Tensile Strength ...... 69
4.3 Modulus of Elasticity and Poisson’s Ratio ...... 73
4.4 Flexural Strength ...... 74
4.5 Reinforced Foamed Concrete Beams ...... 80
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4.6 Sandwich Beams ...... 87
4.7 Compression Columns ...... 92
V. CONCLUSIONS...... 101
5.1 Conclusions ...... 101
5.2 Recommendations ...... 102
REFERENCES ...... 104
APPENDIX ...... 111
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LIST OF TABLES
Table Page
1- Comparison between foamed concrete and plain concrete ...... 7
2- Various application of foamed concrete, Neville, 1985 and [13] ...... 10
3- Chemical composition of cement [2]...... 11
4- Chemical composition of cement, silica fume and fly ash class F ...... 44
5- Properties of polypropylene and basalt fiber ...... 46
6- Mix proportions [2] ...... 47
7- Compressive strength of PFC, PPFC and BFC ...... 67
8- Splitting tensile strength PFC, PPFC and BFC ...... 69
9- Modulus of elasticity for PFC, PPFC and BFC specimens ...... 73
10- Poisson's ratio for PFC, PPFC and BFC ...... 73
11- Flexural strength of PFC, PPFC and BFC ...... 75
12- Maximum load for reinforced PFC, PPFC and BFC specimens ...... 80
13- Maximum load for Styrofoam, PFC, PPFC and BFC sandwich specimens...... 87
14- Maximum load for Styrofoam, PFC, PPFC and BFC column specimens ...... 92
15- Initial mix proportion...... 114
16- Compressive strength for initial mix ...... 114
17- Mix proportion II ...... 115
18- Compressive strength for mix proportion II ...... 115
19- Modified mix proportion ...... 116
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20- Compressive strength of modified mix proportion ...... 116
21- Modified mix proportion II...... 117
22- Compressive strength of modified mix proportion II ...... 117
23- Series 3 initial mix proportion ...... 118
24- Compressive strength series 3 initial mix proportion ...... 118
25- Series 3 mix proportion II ...... 119
26- Compressive strength series 3 mix proportion II...... 119
27- Series 3 mix proportion III ...... 120
28- Compressive strength of series 3 mix proportion III ...... 120
29- Mix proportion for BFC specimen ...... 121
30- Compressive strength of BFC...... 121
31- Series 4 mix proportion I ...... 122
32- Compressive strength series 4 mix proportion I ...... 123
33- Stress vs. longitudinal strain for PFC ...... 124
34- Stress vs. longitudinal strain for PPFC specimen ...... 125
35- Stress vs. longitudinal strain for BFC ...... 126
36- Analysis of reinforced foamed concrete beam ...... 128
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LIST OF FIGURES
Figure Page
1- The Pantheon Dome, LWC application, Rome, built in 126 AD (Wikipedia, Roman Architecture: Concrete Vision) ...... 6
2- Left: Parrotts Ferry Bridge, Right: The Calgary Saddledome Stadium [10] ...... 8
3- Longest double T's [10] ...... 8
4- Miami postal office [11] ...... 8
5- Comparison of normal concrete and LWC floor slabs in tall buildings [4] ...... 9
6- Compressive strength development with increase in fly ash content ...... 12
7- Compressive strength development with age and density [30] ...... 14
8- Strength - density variation for mixes with different sand fines ...... 15
9- Variation of compressive strength with density [2, 18]...... 15
10- Variation of compressive strength with number of days [22, 33] ...... 17
11- Fiber fraction versus compressive strength [34, 35] ...... 17
12- Compressive strength of concrete specimens for 28 and 56 days [12] ...... 18
13- Splitting tensile strength vs. compressive strength [18] ...... 19
14- splitting tensile strength vs. compressive strength [2] ...... 19
15- Splitting tensile strength vs. compressive strength for OPS [36] ...... 20
16- Tensile strength vs. fiber volume fraction [34] ...... 22
17- Splitting tensile strength for various concrete specimens [12] ...... 22
18- Variation of flexural strength with percentage volume of fiber [34, 47] ...... 23
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19- Flexural strength vs. compressive strength, present and previous studies [36] ...... 24
20- Effect of steel and polypropylene fiber on flexural strength [27] ...... 25
21- Flexural strength vs. number of days [22] ...... 25
23- Stress - strain curve of cellular material [52, 53] ...... 27
24- Variation of modulus elasticity with type of aggregate [12] ...... 27
25- Stress - strain curve with different volume fraction of LWC [54] ...... 28
26- Comparison of experimental and ACI 318 - 05 values ...... 28
27- Typical stress - strain curve [55] ...... 29
28- Stress - strain curve for SL1 and SL2 [33] ...... 30
29- Pre-peak stress - strain curve of LWAC made with LTLWA [3] ...... 30
30- Stress - strain curve for confined and unconfined specimens [56] ...... 31
31- Typical load – deflection behavior of NWC and LWC [1] ...... 32
32- Mid span deflection of different beams in group (a) high, (b) Medium and (c) low tensile reinforcement ratio [57] ...... 33
33- Experimental moment – deflection curve for single and doubly reinforced beams [58] ...... 33
34- Strain distribution during loading [58] ...... 34
35- Load – displacement curve for sandwich panel with plain foamed concrete core and fiber reinforced foamed concrete core [5] ...... 34
36- Experimental research on reinforced concrete sandwich beams [58] ...... 35
37- Materials for foamed concrete ...... 43
38- Left: Foam concentrate, Right: Foam generating machine ...... 45
39- Foam output ...... 45
40- Left: Polypropylene fiber, Right: Basalt fiber ...... 46
41- Concrete mixer ...... 48
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42- Specimen with cut surface ...... 49
43- Compression testing machine ...... 50
44- Capping of specimen ...... 51
45- Specimen with compressometer ...... 51
46- Modulus test set – up ...... 52
47- Splitting tensile strength test set - up ...... 53
48- Flexural beam test set - up ...... 55
49- Reinforcement and formwork for RFC beams ...... 56
50- MTS 55 kip frame machine with cameras focused to capture data ...... 57
51- Foamed concrete panel ...... 58
52- Foamed concrete panel with reinforcement on the top of the plain concrete ...... 58
53- Specimens covered by burlap ...... 59
54- Foamed concrete specimen for compression column specimen ...... 60
55- Orientation of foamed concrete panels ...... 60
56- Column specimen showing the method of casting ...... 61
57- Schematic diagram representing sandwich beam – side view ...... 61
58- Schematic diagram representation of sandwich beam - sectional view ...... 62
59- 3D Schematic representation of sandwich beam ...... 63
60- Schematic representation of compression column – front view ...... 63
61- Test set-up for sandwich specimen under bending ...... 64
62- Schematic representation of test set - up of a sandwich specimen ...... 65
63- Test set-up for compression column specimen...... 65
64- Compressive strength vs. unit weight for PFC, PPFC and BFC ...... 67
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65- Failure of PFC, PPFC and BFC ...... 68
66- Left: Failure pattern of BFC; Right: Orientation of fiber in BFC ...... 69
67- Splitting tensile strength vs. unit weight for PFC, PPFC and BFC ...... 70
68- PFC failure at the first crack ...... 71
69- Left: PPFC after failure; right: BFC after failure ...... 71
70- Cut open specimen, PFC, PPFC and BFC ...... 72
71- Stress – strain curve for PFC, PPFC and BFC ...... 74
72- Flexural strength vs. unit weight for PFC, PPFC and BFC ...... 75
73- Failure pattern of left-PFC and right-PPFC ...... 76
74- Failure pattern of BFC ...... 76
75- PFC specimen I, II and III ...... 77
76- PPFC specimen I. II and III ...... 78
77- BFC specimen I, II and III ...... 79
78- Load vs. deflection for PFC, PPFC and BFC ...... 81
79- Failure pattern of PFC specimen ...... 81
80- Bond between rebar and foamed concrete in PFC specimen ...... 82
81- Failure pattern of reinforced plain foamed concrete (PFC) specimen ...... 83
82- Failure pattern of reinforced PPFC specimen...... 83
83- Failure pattern of reinforced BFC specimen ...... 84
84- Bond between rebar and fiber reinforced foamed concrete in BFC ...... 84
85- Failure pattern of reinforced BFC specimen I, II and III ...... 85
86- Load vs. strain for PFC, PPFC and BFC specimen ...... 86
87- Load vs. deflection for Styrofoam, PFC, PPFC and BFC ...... 88
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88- Failure pattern of PFC sandwich specimen ...... 88
89- Failure pattern of BFC sandwich specimen ...... 89
90- Failure Pattern of PFC, PPFC and BFC sandwich specimens ...... 90
91- Bond of the concrete specimen within the sandwich beam ...... 90
92- Different crack width in the individual layer with the sandwich beam ...... 91
93- Load vs. strain for Styrofoam, PFC, PPFC and BFC sandwich specimen ...... 91
94- Compressive load vs. strain for different column specimen with and without reinforcement ...... 93
95- Styro and R - Styro compression column specimens ...... 94
96- PFC and R - PFC compression column specimens ...... 95
97- PPFC and R - PPFC compression column specimens ...... 96
98- BFC and R -BFC compression column specimens ...... 96
99- Failure pattern of unreinforced Styro, PFC, PPFC and BFC under compression ...... 97
100- Failure pattern of reinforced Styro, PFC, PPFC and BFC under compression ...... 98
101- Failure pattern of the specimens due to eccentric loading ...... 98
102- Compressive load vs. strain for reinforced Styrofoam, PFC, PPFC and BFC column specimens ...... 99
103- Compressive load vs. strain for Styrofoam, PFC, PPFC and BFC column specimens ...... 100
104- Left: Stirrer rod, Right: Foamed concrete mixing in 5 gallon bucket ...... 113
105- Specimen showing improper mixing of the ingredients ...... 115
106- Specimen with slightly higher water - cement ratio ...... 116
107- Fiber reinforced foamed concrete ...... 117
108- Failure pattern of PFC ...... 118
109- PPFC specimen with 20% foam volume ...... 119
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110- PPFC specimen with 30 % foam volume ...... 120
111- PPFC specimen with 40 % foam volume ...... 121
112- Failure pattern of BFC specimen ...... 122
113- BFC specimen with 1% fiber dosage ...... 123
114- Failure pattern due to cutting the surface of the specimen ...... 123
115- Formwork for sandwich panels and column specimen ...... 127
116- Sandwich panels and column specimen after casting ...... 127
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LIST OF SYMBOLS
fc compressive strength, MPa or psi t time since casting, days w/c effective water cement ratio p mature porosity
3 ɣcon unit volume weight, t/m
Pr. pore ratio
2 σt , ft, T splitting tensile strength, kg/cm or MPa
2 σck , f compressive strength, kg/cm or MPa fcu, fcy cube compressive strength, MPa
MPa mega pascal
Psi pounds (lb) per square inch
Fst splitting tensile strength of steel fiber HSLWAC, MPa or Psi
Ft splitting tensile strength of plain HSLWAC, MPa vf the fiber volume fraction
Lf/Df aspect ratio
T splitting tensile strength, psi or MPa
P maximum applied load indicated by the testing machine, lbf or N l length, in or mm d diameter, in or mm
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fr flexural strength, MPa or Psi
2 σb flexural strength, kg/cm
R modulus of rupture, Psi or MPa
L span length, in or mm
E young’s modulus, MPa
2 Ec modulus of elasticity of concrete, lb/in or MPa
3 3 Wc unit weight of concrete, lb/ft or kg/m
2 specified 28 – day compressive strength of concrete, lb/in or MPa
Efc modulus of elasticity of fiber aerated lightweight concrete, GPa a depth of stress block, inch
2 As total area of steel bars, in fy guaranteed tensile strength of steel bars, ksi
concrete compressive strength, psi b width of beam, inch
β1 factor c depth of neutral axis, in
Mn nominal moment capacity of the section, kip-ft
Mcr cracking moment, kip-ft d effective depth, in.
4 Ig gross section moment of inertia, in n factor for transformed section kd depth of cracked section compression block, in. h overall height of the beam, in.
Vu nominal shear strength provided by concrete, lb
εt transverse strain determined from the horizontal dial gauge
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εL longitudinal strain determined from the vertical dial gauge
I moment of inertia of the section, in4
ε40 strain at 40% of
ε10 strain at 10% of
I moment of inertia of the section, in4
M bending moment, lb – in f bending stress, psi y distance from the neutral axis, in lb pound
LWC lightweight concrete
FC foamed concrete
PFC plain foamed concrete
PPFC polypropylene fiber reinforced foamed concrete
BFC basalt fiber reinforced foamed concrete
HSLWAC high strength lightweight aggregate concrete
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CHAPTER I
INTRODUCTION
1.1 Background
The material consumed most in the world next to water is concrete. Due to advancement of technology and continuous research in prospective fields, it has been possible for today’s construction industries to innovate new materials and various methodologies in the field of material science that can meet numerous structural and functional demands. One among those is the development of structural lightweight concrete, often called foamed concrete or cellular concrete. Commercial demand for lightweight aggregate concrete (LWAC) has strongly increased in recent years because of its advantages over conventional concrete. Its application is found worldwide ranging from low - rise and high - rise building, bridges to offshore structures [1]. In the recent years, more attention has been paid to the development of lightweight aggregate concrete due to its advantages of being a relatively ‘green’ building material, energy saving and
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environmental – friendly [2, 3]. Sometimes reducing the weight of the structural element becomes necessary rather than focusing on increasing the strength, especially in the heavy structures such as tall buildings and bridges where the self-weight of the structure creates problem for the designers [4]. Another interesting fact is that foamed concrete is light in weight, low cost and easy to manufacture material with good workability and excellent performance in thermal insulation, acoustic insulation, fire resistance, corrosion resistance and shock absorption [5].
1.2 Research Significance
The application of lightweight aggregate concrete is limited due to lack of understanding production of this material and its structural performance [1]. Many researchers and industrialists are paying lot of attention to increase foamed concrete use worldwide. The current problem faced by the designers especially in the high – rise buildings and bridges is the self-weight of structures. According to the 2013 report card on America’s Infrastructure, the total number of bridges present in the United States are nearly 607,380 with an average age of 42 years, nearly 25 percent are defined as structurally deficient. In the future, either a unit or a complete bridge would need replacement due to increasing traffic volume and other structural demands. Replacement of these structurally deficient bridges would cost billions of dollars. In order to reduce the cost and produce better performance concrete, intensive research was conducted on fiber reinforced concrete. It is emphasized that precast box beams in Mill Street Bridge (NH), precast cored slabs in Okracoke Island (NC), precast columns in Edison Bridge (FL),
Lewis & Clark Bridge (OR) and prestressed concrete girders and deck in Graves Avenue
2
over I-4 (FL) reduced the weight by 20 to 25 percent .The net saving with the use of sand
LWC girder was $177 [6]. Therefore, experimental results shows that basalt fiber reinforced foamed concrete (BFC) is light in weight and exhibits similar characteristics as of normal concrete.
1.3 Research Objectives
The main objective of this research is to develop structural fiber reinforced foamed concrete. The objectives include the following:
a. To obtain the optimum mix proportion design for the foamed concrete.
b. To optimize the mechanical properties such as compressive strength, modulus of
elasticity and poisson’s ratio, splitting tensile strength and flexural strength of
plain foamed concrete (PFC), polypropylene fiber reinforced foamed concrete
(PPFC) and basalt fiber reinforced foamed concrete (BFC).
c. To study the structural behavior of steel reinforced PFC, PPFC and BFC.
d. To assess the steel reinforced PFC, PPFC and BFC sandwich panels in
compression and bending.
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1.4 Scope of Thesis
This thesis is organized into 5 Chapters. Chapter 1 gives the general introduction, research significance, research objectives and scope of thesis. In Chapter 2, literature review for materials, design mix proportion and mechanical properties such compression test, modulus of elasticity and poisson’s ratio test, splitting tensile test, flexural test, reinforced foamed concrete beams and sandwich panels test are discussed briefly.
Experimental program such as materials used, preparation of formwork, mixing procedure, casting and demoulding and method of testing were explained in Chapter 3.
Chapter 4 presents the laboratory results and discussion. Chapter 5 describes the conclusions and recommendations for future study from this thesis.
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CHAPTER II
LITERATURE REVIEW
2 .1 Background and Introduction
In this section, the basic understanding of foamed concrete, the history, the characteristics and tests conducted by previous researchers is briefly discussed. Foamed concrete is a type of concrete consisting of cement, fine aggregate and water with homogeneous void or pores created by introducing air in the form of small bubbles [7]. It is also called as lightweight concrete or cellular concrete, which is alike normal concrete but with no coarse aggregate. Since it has been found to be lighter in weight than normal concrete, researchers and industrialists are trying to entirely replace normal weight concrete with foamed concrete. More importantly, it is used as an insulating material, partition wall, filling voids and rehabilitation work. In the modern world due to the development and better understanding of lightweight concrete or foamed concrete, it is now possible to use it as a structural concrete rather than just for partition wall or as insulation material. Approximately 100 years ago, the development of autoclaved aerated
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concrete was successfully done in terms of technology and marketability [2]. In 1923,
Romans started using concrete by entraining air to reduce density; later in 1950’s, Valore presented an overview of foamed concrete. After intensive research in 1970’s, Rudai &
Short and Kinniburgh provided the basic composition, physical properties and uses of lightweight concrete. Over a period of time, there was significant improvement and it has been used world-wide for various applications. Figure 1 shows the lightweight concrete structure that was built in 126 AD.
Figure 1- The Pantheon Dome, LWC application, Rome, built in 126 AD (Wikipedia, Roman Architecture: Concrete Vision)
2.2 Comparison of foamed concrete and plain concrete
The characteristics of foamed concrete and plain concrete are summarized in Table 1.
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Table 1- Comparison between foamed concrete and plain concrete
Parameters Foamed Concrete Plain Concrete Unit weight 35 - 100 psi 140 - 150 psi
Compressive strength 1000 - 4500 psi >4000 psi
Load factor Reduces dead load on structure Has a usual load on structure Strength-weight ratio is Strength-weight ratio Has more strength-weight ratio comparatively less Exhibits higher bending Spalling of concrete takes Fire capacity after exposure to fire place after exposure to fire [8] [9] Concrete incorporated with Thermal Insulation No thermal insulation thermal insulation
2.3 Application
Because of foamed concrete’s property to be lighter in weight, it has phenomenal application for various purposes. Parrotts Ferry Bridge as shown in Figure 2 (left), with a center span of 640 foot was built using structural lightweight concrete, which reduced dead load by 20 percent and construction cost by 10 percent [10]. Also, the Calgary
Saddledome Stadium shown in Figure 2 (right), built for the 1988 winter olympics was built using lightweight concrete to make shipping and erection easier. Figure 3 shows longest double-T’s structural lightweight concrete panels, which were used for building a
Denver car showroom.
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Figure 2- Left: Parrotts Ferry Bridge, Right: The Calgary Saddledome Stadium [10]
Figure 3- Longest double T's [10] Lightweight concrete was used in a Postal Office in Miami which provided sound layer for membrane application. Proper slope was achieved as shown in Figure 4 without forming tapered insulation.
Figure 4- Miami postal office [11]
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Using LWC in construction of tall building reduces the amount of reinforcement and member cross-sections, and foundation size [4]. Ceramsite, an artificial light aggregate has unique feature, large surface area and low density. It is widely used in roads, bridge engineering, housing construction, etc. Structural weight, durability of concrete and resistance to earthquakes can be improved by replacing gravel with ceramsite as the main concrete aggregate in building structure.
Figure 5- Comparison of normal concrete and LWC floor slabs in tall buildings [4]
It can be used in road pavement, as it increases the wear resistance of the road. Also, it is used as a wall material because of the lightweight, high strength, good temperature resistant and sound insulation, fire-resistant and anti-radiation property [12]. Table 2 gives the application of foamed concrete depending on the density.
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Table 2- Various application of foamed concrete, Neville, 1985 and [13]
Density (kg/m3) Applications Lightweight and insulating cements for floor foundation, for heat insulation and slope for flat roofs, rigid floor foundation, tennis court foundation, interspaced concrete filling, raceways insulation; 300 to 600 kg/m3 thermo insulating blocks, steel structures (18 to 36 lb/ft3) fireproofing, tunnels and pipelines compensating mass, dumps, foundation and coverings, land reclamation and consolidation underground cavities, infill and all types of infill where an elevated thermal insulation is required. Stables and pig-sites foundations; industrial 600 to 900 kg/m3 foundations, partition and tampooning (37 to 56 lb/ft3) slabs, ceiling slabs, concrete and lightweight concrete mixed panels. Blocks for outside walls, slabs for 900 to 1200 kg/m3 partitions, concrete and lightweight (57 to 75 lb/ft3) concrete mixed panels for covering, foundations for elastic floors. Prefabricated panels for civil and industrial 1200 to 1700 kg/m3 buildings plugging; walls casting, garden (76 to 106 lb/ft3) ornaments.
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2.4 Materials
Portland cement have the following chemical composition: aluminum oxide, ferric oxide, magnesium oxide, sulfur trioxide, tricalcium silicate, dicalcium silicate, tricalcium aluminate, and tetracalcium aluminofernite [14]. The raw materials and the percentage content of cement, silica fume and fly ash are shown in Table 3.
Table 3- Chemical composition of cement [2] Cement content Silica Oxides Fly ash % Fume Silicon dioxide 21.60 92.40 54.90 Aluminum oxide 4.13 0.80 25.80 ferric oxide 4.57 0.50 6.90 calcium oxide 64.44 0.91 8.70 magnesium oxide 1.06 0.27 1.80 sodium oxide 0.11 - 0.30 Potassium Oxide 0.56 - 0.10 Sulfur trioxide 1.74 - 0.60 Loss on ignition 0.76 2.00 0.20
The use of fly ash in foamed concrete increases the compressive strength. Also, the ratio of splitting tensile strength to compressive strength for foamed concrete with fly ash was found similar to the normal concrete [15]. Class F fly ash as per ASTM C 618 specifications should be used. Strength of foamed concrete increases with decreasing the particle size [16]. With the increase in the fly ash content, strength of foam concrete increases [2]. It can be noticed from Figures 6 that with the increase in the content of fly ash, the strength of cellular concrete increases. Silica fume is used to improve the compressive strength of foamed concrete and accelerates its performance [17].
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Figure 6- Compressive strength development with increase in fly ash content
Concrete foaming agents are of two types [www.CreteFoamer.com]:
(a) Protein based type, is an animal byproduct, in some cases it appears like blood.
(b) Synthetic based type, which is usually derived from petroleum products which is
commonly used in shampoos, detergents and car wash chemicals.
There are two methods for achieving foam in the foamed concrete mix, preformed foaming, which means preparing foaming agent by mixing water beforehand and then aerating to form foam. The other method of obtaining foam is directly mixing foam with concrete [7].
Foam plays a vital role in the yield strength of foamed concrete. Density, flow behavior and strength of foamed concrete depend on the volume of foam [2, 16].
Foaming agent conforming to ASTM C869 specifications should be used. Foaming agent is mixed with water in the ratio of 1:50 [18]. Protein based type foaming agent is diluted with water in the ratio of 1:40 [2]. The lightweight concrete containing adequate amount of air entraining agent is shown to have excellent characteristics including very-high
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workability, low density and good strength [19]. The performance of foam concrete depends on the quality of foam and the mixing procedure.
Water used in preparing both foam and foamed concrete should be potable since organic contamination would have an adverse effect on the quality of foam and concrete produced, which also results in low long-term strength of concrete [20]. If hard water is added in the foaming agent, the mixture requires more foaming agent. Similarly, if soft water is used for the mix, less foaming agent is required to develop foam of desired quality. On the other hand, if cold water is added it makes less foam, if hot water is added that will create more foam than cold water. Lastly, if hot air is added, it tends to break down foam very quickly [www.createfoamer.com]. Since foam concrete is a flowing and self-compacting, the water cement ratio is comparatively higher than for normal concrete, it ranges from 0.4 - 0.8. Water required for the mix usually depends on the composition and admixtures of the mix. If the super-plasticizer is used, then water cement ratio can be lowered. It is important that water cement ratio should be maintained at certain minimum level to ensure that complete hydration of cement takes place.
2.5 Fiber
Fibers help concrete to increase the tensile strength, reduce crack width and modify the mode of failure. Modified polypropylene fiber has prominent effect on flexural strength, also fracture toughness and rate of shrinkage is shown to be reduced
[23]. The compressive strength of steel fiber concrete increased up to 25 percent, splitting tensile strength has proved to be increased by 45 percent, deflection seems to decrease thereby increasing the strength compared to plain concrete [24]. Steel fiber greatly
13
improved splitting tensile strength, flexural toughness, flexural strength, and impact resistance [25]. Polypropylene fiber, steel fiber and water hyacinth (Eichhornia crassipes) fibers showed predominant effect on compressive strength and splitting tensile strength
[26]. The result drawn by using Hybrid steel and polypropylene in lightweight concrete for design of concrete materials with reduced density and enhanced ductility for different application, including construction of high-rise earthquake resistant buildings [27]. Use of polypropylene fiber resulted in 40 percent reduction in the slump flow, increased splitting tensile strength by 14.4 percent and flexural strength by 10.7 percent [28]. Due to presence of polypropylene fibers, shrinkage properties were significantly improved in expanded polystyrene (EPS) [29].
2.6 Compressive Strength
Compressive strength of foamed concrete is an important parameter since various other parameters such as splitting tensile strength, flexural strength are dependent on this quantity. As shown in Figure 7, compressive strength of foamed concrete is influenced by its density and aging.
Figure 7- Compressive strength development with age and density [30]
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For a given density, mix with finer sand yielded higher strength than mix with coarse sand which is shown in Figure 8 i.e. the finer the particle the higher is the compressive strength [16].
Figure 8- Strength - density variation for mixes with different sand fines
The strength of foamed concrete appeared to increase exponentially either with the increase in concrete density or with decrease in foam volume, also silica fume and polypropylene fiber significantly increased the compressive strength as shown in Figure
9. By using the polymer foaming agent, lightweight foamed concrete with more than 180 mm flow value was developed and compressive strength was noted to increase more than the normal foamed concrete [18].
Figure 9- Variation of compressive strength with density [2, 18]
15
The relationship between compressive strength, water - cement ratio and time is expressed as [30, 31]:
fc = 88.04 + 6.569ln(t) – 130w/c (1) where, fc = compressive strength, MPa
t = time since casting, days
w/c = effective water cement ratio
Also, the relationship between the porosity and compressive strength of foamed concrete can be given as [31, 32]:
1.174 3.6 fc = 39.6(ln(t)) (1-p) (2) where, fc = compressive strength, MPa
t = time in days
p = mature porosity
The pore ratio has direct relationship with unit volume weight of the foamed concrete which can be expressed as [18]:
ɣcon = 2.1 – 2.3Pr. (3)
3 where, ɣcon = unit volume weight, t/m
Pr. = pore ratio
The specimens were tested in compression after 7, 28, 60 and 90 days of curing, it was noticed that the compressive strength and density increases with age as shown in Figure
10.
16
Figure 10- Variation of compressive strength with number of days [22, 33]
Compressive strength of fiber - reinforced foam concrete increases with the volume percentage of fiber [34]. Figure 11 shows that for the first two mixes, percentage of super-plasticizer was 2.3 and for the other two mixes percentage super plasticizer were
2.5, it can be noticed that 0.2 percent volume fiber gave the highest strength.
Figure 11- Fiber fraction versus compressive strength [34, 35]
It can be noticed from Figure 11 that lightweight fiber-reinforced concrete without surfactant gave more strength than with surfactant, also with the increases in volume of polypropylene fiber, compressive strength was shown to decrease [35]. Compressive strength of lightweight concrete varied from 42.3 to 55.8 MPa with density ranging from
17
1860 to 1943 kg/m3, four different specimens were prepared: lightweight cold-bonded concrete (LWCC), lightweight bentonite concrete (LWBC), lightweight glass powder concrete (LWGC) and normal weight concrete (NWC). Results showed that lightweight concrete glass powder concrete was closer to normal concrete in terms of compressive strength as shown in Figure 12.
Figure 12- Compressive strength of concrete specimens for 28 and 56 days [12]
2.7 Splitting Tensile Strength
The ratio of tensile strength to compressive strength in lightweight foamed concrete is 0.2 to 0.4, with 19 mm vynylon fiber, which is 1.97 times the usual tensile strength. With 30 mm vynylon fiber, the tensile strength of foamed concrete is 2.04 times the normal tensile strength. Figure 13 shows relationship between compressive strength and tensile strength [18]:
0.5 σt = 1.03(σck) (4)
2 where, σt = splitting tensile strength, kg/cm
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2 σck = compressive strength, kg/cm
Figure 13- Splitting tensile strength vs. compressive strength [18]
The splitting tensile strength of foamed concrete decreases with increase in foam volume, increases with increase in compressive strength as shown in Figure 14. A relationship between splitting tensile strength (plotted along Y - axis) and compressive strength
(plotted along X - axis) was proposed and can be expressed as [2]:
0.66632 ft = 0.5806 x f with polypropylene fiber (5)
0.66401 ft = 0.49858 x f without fiber (6) where, ft = splitting tensile strength, MPa
f = compressive strength, MPa
Figure 14- splitting tensile strength vs. compressive strength [2]
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The splitting tensile strength of oil palm shell (OPS) lightweight concrete ranges from 2.8
– 3.5 MPa and is only 28 percent lower than granite concrete, a relationship was proposed between splitting tensile strength and compressive strength and can be expressed as [36]:
0.5 ft = 0.4887(fcu) (7) where, ft = splitting tensile strength, MPa
fcu = compressive strength, MPa
In Figure 15, eight equations proposed by different researchers have been plotted, it can be noticed that the results from [36] i.e. equation (1) showed improvement in splitting tensile strength.
Figure 15- Splitting tensile strength vs. compressive strength for OPS [36]
0.7 ft = 0.20(fcy) (8) where, ft = splitting tensile strength, MPa
fcy = compressive strength, MPa
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The different equations derived by previous researchers for calculating experimental splitting tensile strength value are as follows:
2/3 ft = 0.20(fcu) [36] [38] (9)
0.5 ft = 0.46(fcy) [36] [39] (10)
2/3 ft = 0.23(fcu) [36] [40] (11)
2/3 ft = 0.51(fcy) [36] [41] (12)
2/3 ft = 0.27(fcu) [36] [42] (13)
0.675 ft = 0.358(fcu) [36] [43] (14) where, ft = splitting tensile strength, MPa
fcy, fcu = compressive strength, MPa
Steel fiber reinforced lightweight aggregate concrete (LWAC) has significantly higher splitting tensile strength than plain LWAC even at low fiber volume [44]. As shown in Figure 16, tensile strength increases with increase in percent fiber volume.
Also, Figure 17 shows the splitting tensile strength for different types of mixes. A relationship was proposed to predict the splitting tensile strength of steel fiber reinforced high strength lightweight aggregate concrete made with expanded clay lightweight aggregate [45],
Fst = 0.94Ft (1-Vf) + 3.02VfLf/Df (15) where, Fst = splitting tensile strength of steel fiber lightweight concrete, MPa
Ft = splitting tensile strength of plain lightweight concrete, MPa
Vf = fiber volume fraction
Lf = length of the fiber, mm
Df = diameter of fiber, mm
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Figure 16- Tensile strength vs. fiber volume fraction [34]
Figure 17- Splitting tensile strength for various concrete specimens [12]
Increase in volume of polypropylene fiber has impact on tensile strength [34]. The 28 day splitting tensile strength of normal weight concrete (NWC) was 6 percent higher than lightweight bentonite concrete (LWBC) and 4 percent higher than lightweight glass powder concrete (LWGC) [12]. The following equation for calculating splitting tensile strength of a specimen is given by [46]:
T = 2P/πld (16) where, T = splitting tensile strength, psi or MPa
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P = maximum applied load, lb or N
l = length, in. or mm
d = diameter, in. or mm
2.8 Flexural Strength
Flexural strength is very important parameter since it governs the use of foamed concrete in structural application. In recent years, studies showed that use of fibers in foamed concrete showed significant improvement [64 – 74]. As shown in Figure 18, modulus of rupture was shown to increase with the increase in volume percentage of fiber.
Figure 18- Variation of flexural strength with percentage volume of fiber [34, 47]
LF1, LF2, LF3, LF4 and LF5 corresponds to the volume percentage of fiber, it can be shown from the graph that LF3 has the maximum flexural strength corresponds to a volume fraction of fiber of 0.35 percent, and fiber length of 12 mm. The flexural strength of oil palm shell (OPS) lightweight concrete depends on the compressive strength. The 28 days flexural strength of OPS was found as 17 percent lower than
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granite concrete. A relationship between the flexural strength and compressive strength was proposed from the experimental results and is expressed as,
1.03 fr = 0.12(fcu) (17) where, fr = flexural strength, MPa
fcu = compressive strength, MPa
Researchers in the past have proposed various relationships between flexural strength and compressive strength, which are as follows:
2/3 fr = 0.3(fcu) [36] [48] (18)
0.5 fr = 0.69(fcu) [36] [48] (19)
2/3 fr = 0.58(fcy) [36] [48] (20) where, fr = flexural strength, MPa
fcu = compressive strength, MPa
Figure 19 (right) gives the flexural strength vs. compressive strength plot for the experiments conducted in the past.
Figure 19- Flexural strength vs. compressive strength, present and previous studies [36]
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Increase in volume fraction of steel and polypropylene fibers in combination or individually with pumice lightweight aggregate concrete improved flexural strength and toughness [27]. Figure 20 shows that higher the percentage of steel and polypropylene fiber combination, higher is the flexural strength.
Figure 20- Effect of steel and polypropylene fiber on flexural strength [27]
The average flexural strength for foamed concrete was noted as 1.43 to 3.80
N/mm2 (200 to 550 psi) as shown in Figure 21.
Figure 21- Flexural strength vs. number of days [22]
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The ratio of flexural strength to compressive strength of foamed concrete was shown to be 0.3 to 0.6 and a relationship between them is expressed from Figure 22
0.5 σb = 1.74(σck) (21)
2 where, σb = flexural strength, kg/cm
2 σck = compressive strength, kg/cm
Figure 22- Flexural strength vs. compressive strength [18] The mix with low water – cement ratio resulted in micro cracks due to incomplete hydration of cement, which results in low flexural strength, and also increase in the fiber volume fraction resulted in higher flexural strength [50, 62]. If the fracture initiates in the tension surface within the middle third of the span length, the modulus of rupture is expressed as follows [51]:
R = PL/bd2 (22) where, R = modulus of rupture, Psi or MPa
P = maximum applied load, lb or N
L = span length, in or mm
b = width of beam, in.
d = effective depth, in.
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2.9 Modulus of Elasticity and Poisson’s Ratio
The compressive stress – strain curve of foamed concrete is divided into three regimes, elastic regime, plateau regime and densification regime as shown in Figure 23.
Figure 23- Stress - strain curve of cellular material [52, 53]
Modulus of elasticity of lightweight bentonite concrete (LWBC) showed better results than lightweight cold-bonded concrete (LWCC) and lightweight glass powder concrete
(LWGC), and is 33 percent lower than normal weight concrete (LWC) as shown in
Figure 24. For the lightweight aggregate concrete, the curvature of the stress-strain decreases with increase in the lightweight content [54]. Modulus of elasticity of fiber reinforced lightweight concrete with no surfactant showed higher results than that of 0.1 percent surfactant [35].
Figure 24- Variation of modulus elasticity with type of aggregate [12]
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Figure 25 shows the stress – strain curve for foamed concrete mix with different percentage of aggreagte. The Young’s modulus of foamed concrete is shown to be 1 to
15 percent of that of normal concrete and a realtionship between modulus of elasticity, density and compressive strength of foamed concrete can be expressed as [18]:
1.5 0.5 E = 6326 (ɣcon) (σck) (23)
3 where, ɣcon = unit weight of concrete, kg/m
2 σck = compressive strength of concrete, kg/m
Figure 25- Stress - strain curve with different volume fraction of LWC [54]
From Figure 26, it can be shown that as the percentage volume of steel fiber of the fiber reinforced foamed concrete increases, the proportionality limit and yield point increases.
Figure 26- Comparison of experimental and ACI 318 - 05 values [35]
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The average value of Poisson’s ratio for lightweight concrete is 0.2 [18]. The addition of fiber were observed to increase in the descending portion of the stress – strain curve as shown in Figure 27.
Figure 27- Typical stress - strain curve [55] According to ACI 318 – 11 the modulus of elasticity can be expressed as
1.5 0.5 EC = 33 (wc) ( ) (24)
3 where, wc = unit weight of concrete, lb/ft
= compressive strength of concrete, psi
From the above equation if the unit weight and compressive strength of concrete are known, the theoretical value for the modulus of elasticity can be predicted. The maximum strain obtained by self-leveling lightweight concrete specimen 1(SL1) and self-leveling concrete specimen 2 (SL2) were 0.0024 and 0.002222 respectively which is less than the strain in normal concrete i.e. 0.003 as shown in Figure 28.
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Figure 28- Stress - strain curve for SL1 and SL2 [33]
In the lightweight aerated concrete, 30 percent expanded clay aggregates have shown relatively higher strength than 40 percent and 50 percent as shown in Figure 29.
Figure 29- Pre-peak stress - strain curve of LWAC made with LTLWA [3]
Confinement of foamed concrete reduces cracks and has shown to give less displacement depending on the wrapping material and condition as shown in Figure 30.
30
Figure 30- Stress - strain curve for confined and unconfined specimens [56]
The modulus of elasticity of fiber aerated lightweight concrete can be expresses as [35]:
-0.8134Ec Efc = 1.259192(1 – e ) (25) where, Efc = modulus of elasticity of fiber aerated concrete, GPa
Ec = modulus of elasticity of concrete, GPa
2.10 Reinforced Foamed Concrete Beam and Sandwich Specimens
Since the aim of the research is to use fiber reinforced foamed concrete as a structural unit, therefore the behavior with steel reinforcement is relatively important parameter that is to be studied. In reinforced concrete beams, tension is resisted by steel and compression is resisted by concrete. In terms of ultimate strength, lightweight aerated foamed concrete showed similar results when compared to normal weight concrete [1].
From Figure 31, it can be noticed that the load vs. deflection curves for lightweight concrete and normal concrete have the same curvature, the initial cracking, yielding of steel. Concrete crushing occurred at about the same level of loading as in the case of beams with normal concrete.
31
Figure 31- Typical load – deflection behavior of NWC and LWC [1]
Investigation was done on ultimate moment and deflection of beams made with lightweight expanded clay aggregate (LECA) and conclusion was drawn to use lighter concrete than using LECA [56]. Figure 32 shows details of the three groups: (a) specimen with high tensile reinforcement ratio, (b) specimens with medium tensile reinforcement ratio and (c) specimens with low tensile reinforcement ratio. It is clear that beams with highest tensile reinforcement ratio have resulted in maximum moment carrying capacity.
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Figure 32- Mid span deflection of different beams in group (a) high, (b) Medium and (c) low tensile reinforcement ratio [57]
The oil palm shell lightweight concrete beams exhibit similar behavior to other lightweight concrete, possess good ductility, showed considerable amount of deflection and achieved full strain capacity under flexural loading [58]. From Figure 33, the moment carrying capacities of singly and doubly reinforced beams with number of specimens are compared. Experiments proved that a lightweight concrete beam which is doubly reinforced has more load carrying capacity than normal concrete beams.
Figure 33- Experimental moment – deflection curve for single and doubly reinforced beams [58]
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The moment and strain data for singly and doubly reinforced beams lightweight concrete are compared in Figure 34. From the plot it is clear that at a particular strain; moment carrying capacity of the doubly reinforced beams are higher than singly reinforced beams for both compression and tension region.
Figure 34- Strain distribution during loading [58] From Figure 35, it can be noticed that plain foamed concrete sandwich panel has attained elastic regime. The sudden drop of the descending part of the curve is due to immediate failure of the specimen, whereas for the fiber reinforced sandwich panel after attaining elastic regime, the beam entered the densified regime [5,63].
Figure 35- Load – displacement curve for sandwich panel with plain foamed concrete core and fiber reinforced foamed concrete core [5]
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Figure 36 describes the experimental research on reinforced sandwich beams carried out in the past by researchers with various loading combinations on the sandwich beams.
Figure 36- Experimental research on reinforced concrete sandwich beams [58]
The theoretical calculations for moment carrying capacity, cracking moment, shear strength and deflection of RFC beams and Sandwich beams are given below:
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Moment carrying capacity: ACI Method
Assumption
Cross section of beam: Rectangular
Crushing strain of concrete, εcu = 0.003 inch/inch
Number layer of bars = 1
Normal weight concrete = 150 pcf
Modulus of elasticity of steel, Es = 29,000 ksi (grade 60 reinforcing steel)
Data
Width of the beam = b, inch
Overall height of beam = h, inch
Effective concrete cover = dc, inch
Tensile strength of steel bars, fy = 60000 psi
Total area of steel bars, As = number of bars x diameter of bar (inch)
Concrete compressive strength, f 'c (from experiment)
Calculations
Effective depth, d = (h - dc)
Factor, β1 = 0.85 (ACI 318 – 11, clause 10.3.7.3)
β1 = for 4,000 psi < < 8,000 psi
β1 = 0.65
Yield strain for steel, εy =
Steel reinforcement ratio, ρ =
Balanced reinforcement ratio, ρb = β1
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Minimum reinforcement ratio, ρmin = or (whichever is maximum)
Maximum reinforcement ratio, ρmax = , for balanced section
ρmax = 0.75ρb (smaller value governs)
ACI maximum steel area, Asmax = ρmax x bd
Depth of Neutral Axis – balanced, cb =
Check the section, ρ > ρb over-reinforced
ρ < ρb under-reinforced
ρ = ρb balanced
Depth of neutral axis, c =
Depth of the stress block, a = c β1
Strain in steel, εt is calculated using the relation:
For over-reinforced beam following calculations should be done,
Factor for over-reinforced section, m =
Ratio of depth of neutral axis to effective depth, =
Check the strain in the steel within the limits, εt < 0.002, compression controlled
0.002 <εt < 0.005, Transition
εt > 0.005, Tension controlled
Nominal moment capacity of the section, Mn =
Strength reduction for the flexure, ɸ = 0.9 if compression controlled
0.65 if tension controlled
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if transition
Design moment capacity, ɸMn
Therefore total load on the beam can be calculated using nominal moment capacity (Mn).
Shear Strength:
(ACI 318-11, Eqaution 11-3) where, Vc = Nominal shear strength provided by concrete, lb
= compressive strength of concrete, psi
bw = web width, in.
d = distance from extreme compression fiber to centroid of longintudinal tension
reinforcement, in.
= 0.75 for lighweight concrete
Cracking Moment:
where, Mcr = cracking moment,lb-in
fr = flexural strength, psi
4 Ig = gross section moment of inertia, in
c = depth of neutral axis, in.
where, fr = flexural strength, psi
λ = 0.75 for lightweight concrete
= compressive strength of concrete, psi
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4 where, Ig = gross section moment of inertia, in
b = width of the beam, in.
h = depth of the beam, in.
Deflection:
Deflection for a beam with two point loading is given by
(for uniformly distributed load)
(for point loads)
where, w = half the total load applied, lb
l = simply supported span, in.
4 Ig = gross section moment of inertia, in
a = shear span, in.
Ec = modulus of elasticity of concrete (psi) which can be calculated as:
where, λ = 0.75 for lightweight concrete
3 wc = unit weight of concrete, lb/ft
= compressive strength of concrete, psi
4 Ie = effective moment of inertia of the section, in , which can be calculated as
follows:
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where, Mcr = cracking moment, lb-in
Ma = total applied moment, lb-in
4 Ig = gross section moment of inertia, in
4 Icr = cracked moment of inertia, in , which can be calculated as follows:
where, b = width of the beam, in.
c = depth of neutral axis, in.
d = distance from extreme compression fiber to centroid of longintudinal tension
reinforcement, in.
n = modular ratio, which is given by
where, Ec = modulus of elasticity of concrete, psi
Es = modulus of elasticity of steel, psi
2 As = area of steel, in
The theoretical calculations for load carried by reinforced and unreinforced columns are calculated by using ACI 318 – 11 equation: 10.3.6,
with = 0.75 for spirally reinforced columns
Since no spiral reinforcment was provided to the column specimen in the experiment, can be neglected. where, Pn = maximun load carried by the specimen, lb
= compressive strength of concrete, psi
2 Ag = gross area of the column, in
2 Ast = area of steel, in
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fy = tensile strength of steel bar, psi
Therefore for the reinforced column specimen, the equation for calculating maximum load carrried by the specimen is given by
For the unureinforced compression column, the equation for calculating maximum load is
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CHAPTER III
EXPERIMENTAL PROGRAM
3.1 Introduction
The details of the experimental works such as the materials used, mix design, mixing procedure, preparation of formwork and the testing procedure are presented in this chapter. At the initial stages of this experiment, different trial mixes were conducted to determine the optimum mix proportion by keeping strength constant. This optimum mix proportion was used to carry out different experimental investigations.
3.2 Ingredients of Foamed Concrete
After performing thorough investigation and based on the research conducted in the past, it was concluded that the use of the finer materials in foamed concrete mix is preferred. Cement, fly ash, silica fume, water reducing plasticizer and fibers were used as shown in Figure 37.
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Silica Fume
Fly ash Cement
Figure 37- Materials for foamed concrete
3.2.1 Cement
Ordinary portland cement (OPC) of brand CEMEXTM Type – I satisfying ASTM
C150 / C150M – 12 specifications was used. The chemical composition is presented in the 1st column of Table 4.
3.2.2 Fly Ash
Class F fly ash supplied by a local ready mix concrete plant. It satisfies ASTM
C618 – 12a. The detail of chemical compositions is given in the 3rd column of Table 4.
3.2.3 Silica Fume
Silica fume supplied by Sika Corporation were used. The chemical composition is given in the 2nd column of Table 4.
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Table 4- Chemical composition of cement, silica fume and fly ash class F Silica Oxides Cement content % Fly ash Fume Silicon dioxide 19.2 95.38 47.17 Aluminum oxide 4.7 0.33 25.61 Ferric oxide 3.0 0.26 19.19 Calcium oxide 62.5 0.55 2.23 Magnesium oxide 4.4 0.17 0.72 Sodium oxide 0.84 0.1 0.45 Potassium Oxide - 0.54 1.88 Sulfur trioxide 3.2 0.15 0.37 Loss on ignition 2.1 2.56 2.37
3.2.3 Foam
Foam concentrate used in this experimental study is CreteFoam CMX brand as shown in Figure 38 and is synthetic based type. They offer much longer shelf life, have no obnoxious odor and perform well under variety of conditions. Foam plays a vital role in foamed concrete, when it is added into the mix; it increases the concrete volume significantly hence decreasing the weight of the mix. The foam usually form the bubbles or voids in the concrete. When the foam evaporates, the bubbles tend to create voids. So, understanding of how bubbles form and evaporate as the concrete hardens is very important issue to be dealt with. The ratio of foam concentrate to water used was 1:50.
Foam generating machine as shown in Figure 38, was used to get the foam output as shown in Figure 39. The process of producing foam was very simple; foam concentrate and water were placed in the pressure container and mixed gently for some time. Then the machine is connected to power and switched on to develop pressure inside the container to produce foam. Foam generating machine has the feature of generating low and high density of foam.
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Pressure Container
Figure 38- Left: Foam concentrate, Right: Foam generating machine
Bentonite and Metakaolin were also used during initial trial mixes, which increased the overall performance of foamed concrete.
Figure 39- Foam output
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3.2.4 Fiber
Polypropylene and basalt fibers were used in this experiment. The properties of these fibers are presented in Table 5.
Figure 40- Left: Polypropylene fiber, Right: Basalt fiber
Table 5- Properties of polypropylene and basalt fiber
Properties Polypropylene Fiber Basalt Fiber [60] Length (mm) 38-54 42-45 Diameter (mm) - 0.66 Density(gm/cc) 0.91 1.8 Rupture strain (in/in) - 0.023 Tensile strength (ksi) 83-96 157
3.2.5 Water
Tap water supplied in the university was used throughout the experiments. This is potable water which has less impurities.
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3.3 Mix Design
Various experiments were conducted to achieve optimum mix proportion. The standard mix design was used for plain foamed concrete (PFC), polypropylene fiber reinforced concrete (PPFC) and basalt fiber reinforced foamed concrete (BFC).
3.3.1 Mix Proportion
The details of mix proportion for PFC, PPFC and BFC are given in Table 6. For all mixes, water - cement ratio was maintained at 0.6 and volume of foam at 20 percent.
Table 6- Mix proportions [2]
Mix Proportion of Foamed Concrete (per 1 cubic-ft) Cement Silica Fly Water Foam w/c Fiber Super- Mix (OPC) fume ash F (lb) volume ratio volume plasticizer (lb) (lb) (lb) (ft3) (%) (lb) PFC 30.7 5.42 36.1 21.7 0.2 0.6 - 0.75 PPFC 30.7 5.42 36.1 21.7 0.2 0.6 0.80 0.75 BFC 30.7 5.42 36.1 21.7 0.2 0.6 0.75 0.75
3.3.2 Mixing Procedure
The ingredients were mixed in the mixer as shown in Figure 41 in the following sequence. At first, the ingredients such as cement, fly ash and silica fume were dry mixed in a concrete mixer. Super plasticizer was mixed in water. Later half of the water of the mix was added to the dry mix and the mixer was made to run until lumps were broken.
Then, remaining half of the water was added and mixed for 2 minutes, foam was added and again mixed for 1 minute, the mix was made to rest for 3 minutes. For the mix design which consists of fibers, they were added at this point of time, again mixed for 2 min.
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Figure 41- Concrete mixer
3.3.3 Casting and Demolding
Casting of foamed concrete specimens is an important step as the results indirectly depend on the output of specimen cast. Necessary steps were taken to ensure effective production of the specimens. Before casting, form oil was applied to the cylinders and molds to make sure concrete will not stick to it. Since, foamed concrete is self - leveling and self – compacting, vibration was not required. After placing of concrete, the surface was leveled to get smooth finish. The specimens were then left to set for 24 hours. The specimens were demolded after 24 hours with necessary tools and were transferred for curing to the curing room.
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3.4 Specimens Preparation and Testing Procedures
3.4.1 Compression Tests
Compressive strength of foamed concrete is an important parameter because it indirectly gives other mechanical properties such as flexural strength, splitting tensile strength and modulus of elasticity. Standard size cylinders of size 4 x 8 inch were used for compression test. Three different batches: PFC, PPFC and BFC were cast with three specimens each for a given mix. Specimens were demolded after 24 hours of casting and kept in the curing room for curing.
Figure 42- Specimen with cut surface
After 7 days, specimens were removed and air dried for at least 24 hours.
Similarly, specimens which are needed to be tested after 28 days were removed from the curing room and dried for 24 hours prior to testing. The specimens were cut at the top to make the surface even as shown in Figure 42. ASTM C39 specification was followed for both casting and testing. The cylinders were tested in the compression testing machine as shown in Figure 43. Specimen size were adjusted in the machine, the rate of loading was
49
maintained between 20000 - 30000 lb/min. Load carrying capacity (lb) and strength (psi) were recorded after the failure of the specimen.
Figure 43- Compression testing machine
3.4.2 Modulus of Elasticity and Poisson’s Ratio Test
For conducting modulus test, standard cylinder of size 6 inches diameter and 12 inches long were cast. After 24 hours of casting, specimens were demolded and kept in a moist curing room. After 28 days of curing, the specimens were air dried for 24 hours and made ready for testing. ASTM C469 specifications were used for casting and testing procedures. ASTM C617 specification for capping the specimens was used as shown in
Figure 44. The specimen was then made to set – up with compressometer as shown in
50
Figure 45. Horizontal and vertical dial gauges were mounted on a compressometer to determine lateral and longitudinal displacement.
Figure 44- Capping of specimen
Figure 45- Specimen with compressometer The set – up was later mounted on a universal testing machine as shown in Figure 46. A load of up to 40 percent of the failure strength of the concrete mix were applied to seat the gauges and subsequently released. Before loading starts, the dial gauges were zeroed.
A small load, approximately 10 percent of the 40 percent compressive strength (0.4 ) was applied, and then readings for both the vertical and horizontal dial gauges and
51
applied load were recorded. The loads at which readings are taken were separated by convenient increments, up to 40 percent. At each load increment, readings for load and both gauges were recorded. The rate of loading was maintained as 5000-6000 lb/min.
Figure 46- Modulus test set – up
For calculating Modulus of Elasticity and Poisson’s ratio, the following equations are used:
(26)
where, σ40 = stress at 40% of
σ10 = stress at 10% of
(27)
where, εt = transverse strain
εL = longitudinal strain
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3.4.3 Splitting Tensile Test
Tensile tests on concrete utilize the split tension test, because direct tension tests on ceramic – based materials are difficult to perform, as there is no practical way to grip the samples. Standard cylinders of size 6 inches diameter and 12 inches long were used for casting and testing the specimens. Three different batches PFC, PPFC and BFC were cast with three specimens each for the given mix. The specimens were tested on a universal testing machine as shown in Figure 47.
Figure 47- Splitting tensile strength test set - up
The rate of loading was 8000 - 9000 lb/min and the maximum load was recorded. The specimens after casting were allowed to set for 24 hours. After 24 hours of casting, the specimens were demolded and kept in a moist curing room. After 28 days of curing, the specimens were removed from the curing room and air dried for 24 hours. Specimens were cast and tested as per the specifications provided by ASTM C496. The foamed
53
concrete specimen was put into the split tension set – up. Each concrete cylinders was laid in a horizontal position, and load was applied to one of the long sides which creates uniform tensile stress in the cylinder. The splitting tensile strength of the specimen can be found out using the equations:
(28) where, ft = splitting tensile strength, psi
P = maximum applied load, lb
d = diameter of the cylinder, in
L = height of the cylinder, in.
3.4.4 Flexural Beam Test
Flexure test was conducted on the foamed concrete to study its flexure behavior.
Standard specimens of size 4 x 4 x 14 inch were cast. Three different batches PFC, PPFC and BFC were cast with three specimens each for the mix. The casting and testing procedure as per the specifications provided by ASTM C78 were followed. After casting of the specimens, they were allowed to set for 24 hours. After 24 hours, the specimens were demolded and transferred to moist curing lab. The specimens were then removed after 28 days curing and air dried for 24 hours before testing. It was then ground in the corners to make the surface even. The specimens were rested on the supports with a clear span of 12 inches. The testing was performed on a universal testing machine at an average rate of loading 30-50 lbs/sec as shown in Figure 48.
The flexural strength was calculated using the following equation:
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(29) where, = bending moment, lb-in
I = moment of inertia of the section, in4
f = bending stress, psi
y = distance from the neutral axis, in
According to ACI 318 – 11, modulus of rupture is given by:
(30) where, fr = flexural strength, psi
λ = 0.75 for lightweight concrete
= compressive strength, psi
Figure 48- Flexural beam test set - up
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3.4.5 Reinforced Foamed Concrete Beam Tests
The purpose of doing this test is to study the performance of foamed concrete with steel reinforcement. Steel molds of size 6 x 4 x 20 inches were prepared as shown in
Figure 51. Reinforcing bars of #3 size were used and the reinforcement was provided only at the bottom as shown in Figure 49. The reinforcing bars were supported laterally to keep them in-place. Three different batches PFC, PPFC and BFC were cast with three specimens each for the mix. The molds were first applied with form oil and later foamed concrete was placed as shown in Figure 49 (right). The specimens were allowed to set for
24 hours. After 24 hours, the specimens were demolded and kept in the moist curing room. After 28 days of curing, the specimens were removed and air dried for 24 hours.
Reinforced foamed concrete beams were tested under three point bending as per ASTM
C78 specifications.
Figure 49- Reinforcement and formwork for RFC beams
The specimens were tested with a MTS 55 kip frame machine as shown in Figure
50. Dots were made on the specimen to capture strain and deflection data. The rate of loading for the machine was 25 lb/sec. When the load is applied on the specimen, the painted dots tend to translate which is recorded in a camera system. The movement of the
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dots recorded were later analyzed using ARAMIS software to get strain and displacement data.
Figure 50- MTS 55 kip frame machine with cameras focused to capture data
3.4.6 Sandwich Beam and Compression Column Tests
Sandwich panels were made to study the behavior of foamed concrete – plain concrete composition. Eight specimens with reinforcement, two of each type were cast with the following combination:
a. Plain concrete – Styrofoam – plain concrete
b. Plain concrete – PFC – plain concrete
c. Plain concrete – PPFC – plain concrete
d. Plain concrete – BFC – plain concrete
At first, foamed concrete core of size 12 x 2 x 30 inches were prepared as shown in
Figure 51. The specimens were allowed to set for 24 hours and demolded. The foamed
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concrete precast panel was inserted within the steel reinforcement as shown in Figure 54 to make the sandwich panel. For making sandwich beams, at first the concrete was filled up to a level of 2 inches from the bottom and then foamed concrete with reinforcement was placed as shown in Figure 52. Plain concrete was placed at the top of precast foamed concrete panel. The complete geometry of the sandwich panel is shown in Figure 57. The required number of sandwich beams were made in this manner. The specimens were later covered with burlap (Figure 53). The test specimens were allowed to set for 24 hours and later demolded and transferred to moist curing room.
Figure 51- Foamed concrete panel
Figure 52- Foamed concrete panel with reinforcement on the top of the plain concrete
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Figure 53- Specimens covered by burlap Compression column sandwich specimens were prepared to study the characteristics of columns under compression. Sixteen columns were prepared out of which eight specimens were with reinforcement and eight were without reinforcement (in pairs). The combinations of column specimens were as follows:
a. Plain concrete – Styrofoam – plain concrete
b. Plain concrete – PFC – plain concrete
c. Plain concrete – PPFC – plain concrete
d. Plain concrete – BFC – plain concrete
e. Reinforced, Plain concrete – Styrofoam – plain concrete
f. Reinforced, Plain concrete – PFC – plain concrete
g. Reinforced, Plain concrete – PPFC – plain concrete
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h. Reinforced, Plain concrete – BFC – plain concrete
Initially, foamed concrete core of size 6 x 2 x 12 inches were prepared as shown in Figure
54. These specimens were allowed to set for 24 hours and then demolded. Foamed concrete panels were placed upright as shown in Figure 55 to make the whole sandwich panel.
Figure 54- Foamed concrete specimen for compression column specimen
Figure 55- Orientation of foamed concrete panels
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For making compression column specimens, at first the concrete was filled on the sides
up to a level of 1 inches and then #3 rebar was placed on the top of concrete, after which concrete was again placed for 3 inches. #3 rebar was placed with concrete on the top to make complete the sandwich test specimen. The required number of column specimens was made in this manner. The specimens were later covered with wet burlap. They were allowed to set for 24 hours and later demolded and transferred to moist curing room.
Figure 56 shows casting of the column specimen.
Figure 56- Column specimen showing the method of casting
#3 rebar wi
Figure 57- Schematic diagram representing sandwich beam – side view
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The sandwich panel was divided into three layers, first layer consist of normal concrete, second layer, the core with foamed concrete and third layer as normal concrete. The broken line indicates the reinforcement i.e. #3 rebar at 5 inches o/c as shown in Figure
57. It is an elevation view with reinforcement details. Figure 58 represents the cross – section view.
#3 rebar at 5’’ o/c
Figure 58- Schematic diagram representation of sandwich beam - sectional view
Also, Figure 59 gives 3 – dimensional view of sandwich beam and Figure 60 gives the front view of column specimen.
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Plain Concrete
#3 rebar wi FC core
Figure 59- 3D Schematic representation of sandwich beam
#3 rebar wi
Figure 60- Schematic representation of compression column – front view
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The specimens were tested using a MTS 55 kip frame machine as shown in Figure 61.
Dots were made on the specimen to capture strain and deflection data. The rate of loading for the machine was 25 lb/sec. When the load is applied on the specimen, the painted dots tend to translate, which is recorded in the high speed camera system. The movement of the dots recorded were later analyzed using ARAMIS software to get strain and displacement data.
Figure 61- Test set-up for sandwich specimen under bending
Also Figure 62 represents schematic representation of sandwich specimen under bending. The supports were placed at 2 inches from the end and load was applied at 4 inches center to center at the mid span as shown in Figure 61.
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(Bearing Plates, spaced at 4 inch o/c)
Figure 62- Schematic representation of test set - up of a sandwich specimen
The specimens were tested using a 300,000 lb capacity universal testing machine as shown in Figure 63. Dots were made on the specimen to capture strain and deflection data. The rate of loading for the machine was 120 - 180 lb/sec. When the load is applied on the specimen, the painted dots translate which is captured in the high speed cameras.
The movements of the dots recorded were later analyzed using ARAMIS software to determine strain and displacement data.
Figure 63- Test set-up for compression column specimen
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CHAPTER IV
RESULTS AND DISCUSSION
This chapter presents the results for the various tests conducted on PFC,
PPFC and BFC specimens in the laboratory. The results include the summary of mechanical properties such as compressive strength, modulus of elasticity and poisson’s ratio, splitting tensile strength, flexural strength of RFC beams. The test results of the sandwich panels in bending and compression are also discussed in the later sections of this chapter.
4.1 Compressive Strength
The compressive strength versus unit weight plot for PFC, PPFC and BFC is presented in Figure 64. It can be noticed that compressive strength of PFC with density
90 – 94 lb/ft3 ranges from 3600 – 3900 psi, while that of PPFC with density 92 – 102 lb/ft3 varies from 3600 – 3800 psi and for BFC with density 100 – 104 lb/ft3 ranges from
5000 – 5500 psi. It can be noticed that PFC and PPFC have almost same compressive
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strength while BFC possess higher compressive strength. BFC has maximum compressive strength among the three.
Table 7- Compressive strength of PFC, PPFC and BFC
PFC # Unit Weight (lb/ft3) Failure Load (lb) Strength (psi) 1 92.8 48870 3888 2 92.8 46520 3700 3 91.1 45680 3635 PPFC # Unit Weight (lb/ft3) Failure Load (lb) Strength (psi) 1 99.7 47530 3782 2 98.0 45240 3600 3 101.4 47900 3811 BFC # Unit Weight (lb/ft3) Failure Load (lb) Strength (psi) 1 103.1 68960 5487 2 101.4 72750 5789 3 101.4 67110 5340
7000
6000
5000
4000
3000
2000 PFC BFC Compressive Compressive Strength (psi) 1000 PPFC 0 90 92 94 96 98 100 102 104 Unit Weight (lb/ft3)
Figure 64- Compressive strength vs. unit weight for PFC, PPFC and BFC
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From Figure 65, PFC specimens failed in shear while for the PPFC and BFC specimens were noticed to fail with cracks extended to mid-half of the height of the cylinder, it was not a uniform crack pattern as for PFC. Moreover, after the failure of PPFC and BFC specimens, spalling of concrete was not noticed, but for PFC small pieces of concrete were falling apart.
Figure 65- Failure of PFC, PPFC and BFC
The failure pattern of the BFC specimen resembles completely different from PFC specimens. The failure can be noticed only at particular region as shown in Figure 66
(left), all the specimens were noticed to have similar failure pattern. Figure 66 (right) shows the random orientation of basalt fibers in the BFC specimen, most of the fibers are noticed to be oriented parallel to longitudinal direction, which is helpful in carrying tension.
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Orientation of Fibers
Figure 66- Left: Failure pattern of BFC; Right: Orientation of fiber in BFC
4.2 Splitting Tensile Strength
Table 8 gives the value of splitting tensile strength of PFC, PPFC and BFC specimen.
The experimental results give higher values when compared with the value calculated by using equations (28), (4), (5), (6) and (7).
Table 8- Splitting tensile strength PFC, PPFC and BFC
Theoretical Specimen 1 Specimen 2 Specimen 3 Average Value (psi) (psi) (psi) (psi) (psi) PFC 299.3 326.4 264.7 296.8 244 PPFC 468.6 453.6 525.3 482.4 140 [5] BFC 713.9 620.2 650.0 661.3 -
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Splitting tensile strength vs. unit weight plot for PFC, PPFC and BFC is presented in
Figure 67. It can be seen that splitting tensile strength are different for all the three specimens. For unit weight of 93 lb/ft3, the splitting tensile value for PFC is around 300 psi, it is 450 psi for PPFC and 600 psi for BFC. The splitting tensile strength of basalt foamed concrete is maximum when compared to PFC and PPFC.
750.00
600.00
450.00 PFC PPFC 300.00 BFC 150.00
0.00 92.8 92.8 91.1
Figure 67- Splitting tensile strength vs. unit weight for PFC, PPFC and BFC
Figure 68 shows the failure mode of PFC under splitting tensile test loading. At the first crack, PFC was noticed to fail completely; the cracking load and the yielding load were observed to be the same for this specimen. For PPFC, the first crack was noted to be similar with PFC, but specimens were observed to carry at least 50 percent more stress after the initial crack. Similarly, the initial crack observed for BFC was at the same load as that of PFC, but the stress carried by the specimen after first crack was observed to be
100 percent more than PFC.
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Figure 68- PFC failure at the first crack
The PPFC and BFC specimen, even after application of maximum load, did not fail completely, fibers were holding them together as shown in Figure 69. On PPFC specimen fibers were exposed, but on BFC specimen, only cracks were observed and the specimen stayed mostly intact, proving that BFC specimen performed much better than
PFC and PPFC specimens.
Figure 69- Left: PPFC after failure; right: BFC after failure
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The test specimens after failure were crushed to cut open to view the failure surface. It was hard for the BFC to break into two pieces. Basalt fibers were well bonded to the concrete on both sides of the failed surface, indicating the superior effectiveness of this fiber. Figure 70 shows the distribution and orientation of the fibers in PPFC and BFC.
Figure 70- Cut open specimen, PFC, PPFC and BFC
The failure plane for PFC was noticed to be straight i.e. exactly at the center, while the plane of failure for PPFC varied slightly from the center line and for BFC the plane of failure was noticed to be irregular. The distribution of fiber for PPFC and BFC was observed to be uniform all along the longitudinal cross – section. Some of the fibers were noticed to be oriented vertically and some inclined at an angle, but most of the fibers were noticed to be parallel.
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4.3 Modulus of Elasticity and Poisson’s Ratio
From Table 9, the experimental value of modulus of elasticity and poisson’s ratio for PFC, PPFC and BFC are 1.08 x 106 psi, 1.33 x 106 psi and 1.41 x 106 psi respectively.
These values are closer to the value calculated using ACI formula i.e. equation (24) and higher than equations (23) and (25). The modulus of elasticity of BFC is closest to ACI value when compare to PFC and PPFC specimen.
Table 9- Modulus of elasticity for PFC, PPFC and BFC specimens
Unit weight Experimental value ACI Code (psi) Specimen Type (lb/ft3) (psi) x 106 x 106
93.0 1.1 1.4 PFC 93.0 1.1 1.3 91.0 1.1 1.3 1.1 1.3 98.0 1.4 1.5 PPFC 101.0 1.3 1.6 93.0 1.3 1.3 1.3 1.4 103.0 1.4 1.6 BFC 103.0 1.6 1.9 103.0 1.2 1.6 1.4 1.7
Poisson’s ratios of different specimens are listed in Table 10. For PFC, PPFC and BFC, the value of Poisson ratio is 0.26, 0.24 and 0.21 respectively.
Table 10- Poisson's ratio for PFC, PPFC and BFC
Specimen Type Experimental Value PFC 0.26 PPFC 0.24 BFC 0.21
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The compressive stress versus strain plot is shown in Figure 71, it can be seen that that
PPFC and BFC exhibit almost similar stress – strain curve. For a particular strain i.e.
0.0003, the stress carried by PFC is 300 psi, stress by PPFC is 415 psi while stress carried by BFC is 440 psi. At higher strain i.e. 0.0005, the stress carried by PFC, PPFC and BFC are 525 psi, 700 psi and 725 psi respectively. BFC exhibit marginally higher stress carrying capacity than PFC and PPFC for any particular strain.
900
750
600
450
Stress Stress (psi) 300 PFC BFC 150 PPFC 0 0 0.0002 0.0004 0.0006 0.0008 Strain
Figure 71- Stress – strain curve for PFC, PPFC and BFC
4.4 Flexural Strength
Table 11 gives the flexural strength of PFC, PPFC and BFC specimens. It can be seen that the average flexural strength for PFC, PPFC and BFC specimens are 67 psi, 392 psi and 690 psi respectively. The flexural strength values for PPFC and BFC is higher than the values calculated by using ACI equation (30) and equations (17), (18), (19) and
(20).
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Table 11- Flexural strength of PFC, PPFC and BFC
Specimen Specimen 1 Specimen 2 Average ACI 3 (psi) (psi) (psi) (psi) (psi)
PFC 76.9 73.2 82.5 67.5 344.1 PPFC 439.9 355.3 320.4 392.6 346.5 BFC 854.5 607.3 652.0 691.0 397.6
Flexural strength vs. unit weight plot for PFC, PPFC and BFC is illustrated in Figure 72.
From the Figure, it can be observed that the flexural strength of fiber-reinforced foamed concrete is very high compared to plain foamed concrete in particular for basalt fiber reinforced foamed concrete. BFC shows nearly 10 times the strength of PFC.
Flexural Strength 900
750
600 PFC 450 PPFC 300 BFC
150
0 92.8 92.8 91.1
Figure 72- Flexural strength vs. unit weight for PFC, PPFC and BFC
As shown in Figure 73, the failure pattern of foamed concrete PFC and PPFC are not similar. PFC specimens were shown to fail after first crack, mostly in shear. PPFC the specimens were noticed to have more cracks with significant load carrying capacity.
Multiple cracks were noticed at the surface of the specimen with maximum crack width
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of quarter inch. The specimens failed in flexure. Even after the specimen developed cracks, the beam was able to sustain the load.
Figure 73- Failure pattern of left-PFC and right-PPFC
BFC was noticed to have initial crack similar to PPFC, but its load carrying capacity was much higher than PFC and PPFC. Many cracks were observed under loading as shown in Figure 74. The maximum crack width was less than PPFC specimen, and crack spacing was even with evenly distributed cracks. The beam was noticed to fail in flexure. Again the flexural strength of BFC was noticed to be maximum when compared to that of PFC and PPFC beams.
Figure 74- Failure pattern of BFC
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Figure 75 shows the failure mode of PFC specimens. Specimen I, specimens II and III was noticed to fail in flexure. The three specimens had single crack failure at mid
- section.
Figure 75- PFC specimen I, II and III
For PPFC specimens, specimen I and IV had similar failure pattern, and specimens II and III was noted to have same failure mode. Specimen I, as shown in
Figure 76, had equal crack spacing and failed in flexure. Specimen II was noticed to have single crack opening and failed in flexure. Specimen III resembles the same failure pattern as that of specimen II. Single crack was noticed at mid half of the surface.
Specimen IV was noticed to have two cracks, one at the center and other at the left portion of the specimen, the middle crack was wider than other cracks located in the left portion of the specimen. PPFC specimens were noted to have fewer cracks than BFC
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specimen and wider crack. However, PPFC specimens have smaller load carrying capacity than BFC specimens.
Figure 76- PPFC specimen I. II and III
For BFC specimens, specimen I, III and IV shows similar failure pattern, specimen II had slightly different failure mode than other specimens. Specimen I as shown in Figure 77 had unequal crack spacing; multiple cracks were noticed with crack width less than crack width of PPFC and ultimately the specimen failed in flexure.
Specimen II was noticed to have single crack opening with small hairline cracks over the surface of the beam and it is noted to fail in flexure. Specimen III shows the same failure pattern as that of specimen I, multiple cracks were noticed on the surface. Specimen IV was noted to have two cracks one at the center and other at the left portion of the
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specimen, the middle crack width is wider than other crack located at the left portion of the specimen. The specimen ultimately failed in flexure. From the flexural strength tests, it can be noted that basalt fiber reinforced foamed concrete (BFC) have multiple hair cracks with lesser crack width which implies that the specimen can still undergo deformation and hence can carry more load. Its failure mode is more ductile than that of
PPFC and PFC beams.
Figure 77- BFC specimen I, II and III
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4.5 Reinforced Foamed Concrete Beams
Since the goal of the experimental program was to use foamed concrete in structural applications, Table 12 lists individual results. The average maximum load carried by PFC, PPFC and BFC are 4314 lbs., 8011 lbs. and 8508 lbs. respectively.
PPFC and BFC had the load carrying capacity which is nearly twice of PFC.
Experimental shear strength value was shown to be higher than the theoretical shear strength value calculated using ACI formula.
Table 12- Maximum load for reinforced PFC, PPFC and BFC specimens
Specimen Maximum Theoretical Shear Failure Pattern Type Load (lb) Strength (lb) PFC 4314 1651 Shear PPFC 8011 1663 Shear BFC 8508 1908 Shear
Figure 78 illustrates the load vs. deflection plot for PFC, PPFC and BFC specimens. It can be noticed that at a given deflection, load carried by PFC, PPFC and BFC are different. For instance, at 0.05 inches deflection, the load carried by PFC is around 1800 lbs, for PPFC is around 3200 lbs and for BFC specimen it is around 3250 lbs. PFC was recorded to carry maximum load of 4314 lbs with 0.115 inches deflection. After PFC,
PPFC specimens were noted to carry maximum load i.e. 8011 lbs with 0.2 inches deflection and BFC was observed to carry maximum load of 8508 lbs among the three with 0.17 inches deflection.
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Load vs Deflection 10500.0 9000.0 7500.0
6000.0 PFC 4500.0 BFC Load (lb) Load PPFC 3000.0 ACI-Theoretical 1500.0 Experimental E 0.0 0 0.05 0.1 0.15 0.2 0.25 Deflection (in)
Figure 78- Load vs. deflection for PFC, PPFC and BFC
From Figure 79, the PFC specimens showed multiple cracks on the left half portion of the specimen. Spalling of concrete took place immediately after failure of the specimen. The specimen was observed to have failed in shear.
PFC Beam
Figure 79- Failure pattern of PFC specimen
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Figure 80 shows the bond between the rebar and foamed concrete. It was noticed that the bond was not good which may be due to the use of larger diameter bar. In normal concrete, when the specimen is loaded, transfer of load happens from concrete to rebar due to bond at the concrete – rebar interface. But for PFC, it was noticed that immediately after failure the spalling of concrete was taking place and very little transfer of load was noticed due to the lack of bond.
Figure 80- Bond between rebar and foamed concrete in PFC specimen
Figure 81 shows the details of failure pattern. It can be noticed that concrete was falling apart immediately after failure. Specimen I shows that crushing of concrete took place, and for specimen II, there was no bond between concrete and rebar after crushing of the specimen.
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Inadequate Bond
Figure 81- Failure pattern of reinforced plain foamed concrete (PFC) specimen
PPFC specimens as shown in Figure 82 were observed to have minor cracks on the surface except at the point of failure. The specimen was noticed to fail in shear with much larger crack width. Spalling of concrete was also observed in these specimens.
PPFC Beam
Figure 82- Failure pattern of reinforced PPFC specimen
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From Figure 83, BFC specimens were shown to have multiple cracks on the left half portion of the specimen. Spalling of concrete did not take place immediately after failure of the specimen as in PFC beams. The specimen was observed to fail in shear.
BFC Beam
Figure 83- Failure pattern of reinforced BFC specimen Figure 84 shows the bond between the rebar and foamed concrete, it was noticed that the bond does not seems to be perfect which can also be due to the use to larger diameter bar.
Figure 84- Bond between rebar and fiber reinforced foamed concrete in BFC
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In normal concrete, transfer of load happens from concrete to rebar which results in carrying more load by specimen if it develop good bond at the concrete – rebar interface.
The other issue for the bond would be absence of coarse aggregate. BFC beams were able to carry maximum load among the three specimens. Load transfer seemed to take place due to presence of bond. Figure 85 gives the failure pattern of BFC beams. It can be noticed that there was transfer of load from concrete to reinforcement and smaller amount of spalling of concrete. Specimen I, II and III failed in similar manner. Since fibers were present within the concrete, the specimen was stiff and fiber helped concrete not to fall apart or crumble.
Figure 85- Failure pattern of reinforced BFC specimen I, II and III
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Figure 86 shows the load versus strain plot for PFC, PPFC and BFC specimens. It is clear that among PFC, PPFC and BFC, the load carrying capacity for a particular strain is maximum in both tension and compression regions for BFC. The maximum strain developed in PFC was nearly 0.00075, while for PPFC the maximum strain was 0.0013, and for BFC the maximum strain recorded was 0.0019. In the tensile region, at 0.001 strains, the load carried by PPFC was observed to be 5,000 lbs and for BFC it was observed around 7,000 lbs. In the compression region, maximum strain developed in the
PFC specimen was 0.0018. It was 0.0027 for PPFC specimens and for BFC, the maximum strain reported was 0.0015. For 0.001 strains, the maximum load carried by
PFC was 1,750 lbs. The load recorded was around 5,000 lbs for PPFC, and for BFC, it was 7,000 lbs.
Load vs Strain C - Compression 10000 T - Tension
8000
6000 PFC-T
Load(lb) PPFC-T 4000 BFC-T PFC-C 2000 PPFC-C BFC-C 0 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 Strain
Figure 86- Load vs. strain for PFC, PPFC and BFC specimen
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4.6 Sandwich Beams
The maximum load carried by Styrofoam, PFC, PPFC and BFC specimens are 7,120 lb,
10,150 lbs, 14,050 lbs and 18,150 lbs is shown in Table 13. PPFC and BFC had a load carrying capacity which is nearly double of PFC. Among the sandwich specimens, BFC was noticed to have largest load carrying capacity. Experimental shear strength value was shown to be higher than the theoretical shear strength value calculated using ACI formula.
Table 13- Maximum load for Styrofoam, PFC, PPFC and BFC sandwich specimens
Maximum Load Theoretical Shear Specimen Type Failure Pattern (lb) Strength (lb)
Styrofoam 7120 5857 Shear PFC 10150 6345 Shear PPFC 14050 7022 Shear BFC 18150 7150 Shear
Figure 87 illustrates the load vs. deflection plot for Styrofoam, PFC, PPFC and BFC specimens. It can be noticed that at a certain deflection, the load carried by all the four specimens are different. For instance, at 0.02 inches the load carried by Styrofoam sandwich and PFC specimen is around 2,500 lbs, for PPFC the load is around 12,500 lb; and for BFC specimen, the corresponding load was 4,000 lbs. Similarly at 0.037 inches,
Styrofoam carried 5,000 lbs, PFC carried a load of 3,500 lbs, PPFC and BFC carried a load of 13,500 lbs. BFC was observed to carry maximum load among the three with 0.05 inches deflection.
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Load vs. Displacement 21000
18000
15000
12000 Styrofoam PFC 9000 Load (lb) Load PPFC 6000 BFC
3000 ACI Experimental E 0 0.00 0.10 0.20 0.30 0.40 0.50 Displacement (in.) Figure 87- Load vs. deflection for Styrofoam, PFC, PPFC and BFC
From Figure 88, it can be seen that extensive spalling took place for PFC specimens immediately after failure of the specimen. The specimen was observed to fail in shear.
Figure 88- Failure pattern of PFC sandwich specimen
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Figure 89 shows failure pattern of BFC specimen. Initially flexure cracks were noticed on left half portion of the specimen. Concrete spalling took place immediately after the failure of the specimen. When the specimen was loaded, the sandwich beam did not act as a homogeneous unit. The load was carried as an individual layer followed by failure of one layer after the other as shown in Figure 89. Moreover, there was no bond between the plain concrete and foam concrete panel within the sandwich beam. The specimen failed in shear.
Figure 89- Failure pattern of BFC sandwich specimen Figure 90 shows the failure pattern of the individual specimens. It was noted during the experiment that homogeneity was not achieved during the loading. Transfer of load from one layer to the other was not very effective. Cracks were noticed in the individual layer within the sandwich beams. PFC specimen I and II, PPFC specimen I and II, and BFC specimen I and II had similar failure pattern. Since fibers were not present in the outer layers of sandwich beams, extensive spalling of concrete took place.
All the specimens failed in shear.
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Figure 90- Failure Pattern of PFC, PPFC and BFC sandwich specimens Figure 91 shows the lack of bond between the plain concrete and foamed concrete panel within the sandwich beams. Inadequate bond may result in the lack of integrity in the panels and lower load carrying capacity.
Figure 91- Bond of the concrete specimen within the sandwich beam
It can be seen from Figure 92 that the sandwich beams did not act as a homogeneous beam, but acted as stacked layers. Different crack widths in the individual layers are the
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evidence for that behavior. Also, it was noticed that immediately after failure the spalling of concrete took place and non - uniform transfer of load was noticed due to inadequate bond.
Figure 92- Different crack width in the individual layer with the sandwich beam
Figure 93 shows the load vs. strain plot for Styrofoam, PFC, PPFC and BFC specimens. The maximum strain carried by Styrofoam was 0.00175, for PFC it was nearly 0.0011, while for PPFC, the maximum strain was as 0.0013; for BFC, the maximum strain was 0.0028 in the tensile region.
Load vs Strain C - Compression 20000 T - Tension 17500 BFC-C 15000 BFC-T
12500 PPFC-C 10000 PPFC-T
Load (lb) Load 7500 PFC-C
5000 PFC-T
2500 Styro-C Styro-T 0 -0.002 -0.001 0 0.001 0.002 0.003 Strain
Figure 93- Load vs. strain for Styrofoam, PFC, PPFC and BFC sandwich specimen
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4.7 Compression Columns
Table 14 gives the maximum load carried by reinforced and unreinforced Styrofoam,
PFC, PPC and BFC specimen.
Table 14- Maximum load for Styrofoam, PFC, PPFC and BFC column specimens
Specimen Maximum Failure 1st Crack Comment Type Load (lb) Pattern Styro 51300 26400 splitting - R-Styro 58656 - splitting - wider cracks & PFC 92000 40000 buckling spalling of concrete R-PFC 94000 - buckling fewer, narrow cracks PPFC 92000 50000 splitting wider cracks R-PPFC 91500 - buckling fewer hair cracks BFC 93000 50000 splitting fewer wider cracks R-BFC 91000 - buckling fewer hair cracks
Figure 94 shows the load vs. deflection plot for Styrofoam, PFC, PPFC and BFC specimens with and without reinforcement. The solid line in the plot indicates reinforced specimen and broken line indicates unreinforced specimen. It can be noticed that at a certain deflection, the load carried for reinforced and unreinforced specimens are different. For instance, at 0.05 inches deflection, the load carried by unreinforced
Styrofoam specimen is 21,000 lbs and reinforced Styrofoam is 40,000 lbs. For PFC specimen, the corresponding load was 40000 lbs for unreinforced PFC specimen and for reinforced PFC is around 70000 lbs. For PPFC specimen, the load carried is around
30000 lbs for unreinforced PPFC specimen and for reinforced PPFC is 42000 lbs. And for BFC specimens, the load carried is around 38000 lbs for unreinforced BFC specimen
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and for reinforced BFC is 58000 lbs. For both, without reinforced and reinforced specimens, PFC was noticed to carry maximum load among four specimen.
Load vs Displacement in Y 120000
R-BFC 100000 BFC 80000
R-PPFC
60000 PPFC
Load (lb) Load R-PFC 40000 PFC
20000 R-styro Styro 0 0.00 0.05 0.10 0.15 0.20 Displacement (in)
Figure 94- Compressive load vs. strain for different column specimen with and without reinforcement
Figure 95 gives the description of failure pattern of Styrofoam specimen without and with reinforcement. Unlike other specimens, in the Styrofoam specimen, initial crack was noticed for both Styro and R – styro specimens at the same load. Styro specimen immediately after initial crack, split into different layers as shown in Figure 95 and had a wider crack width. On the other hand, R – styro specimen, had fewer cracks and lesser crack width. It was noticed that under the loading, specimen acted as a homogeneous unit and did not split into layers due to presence of reinforcement. The load carried by Styro and R – styro were almost the same.
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Figure 95- Styro and R - Styro compression column specimens
Figure 96 shows the failure pattern of PFC specimen without and with reinforcement. For the PFC specimen, initial crack was noticed at 40,000 lbs and specimen split into individual layers. The specimen carried load even after failure and the maximum load carried by the specimen was about 90,000 lbs. There was no bond between the foamed concrete panel and plain concrete panel within the column specimen. For R – PFC specimen, the crack was noticed at the maximum load i.e. 94,000 lbs. Crack was noticed at the plain concrete and foamed concrete intersection; and had smaller crack width.
Spalling of concrete took place and under the loading, the specimen acted as a homogeneous unit and did not split into layers due to presence of reinforcement. The load carried by PFC and R – PFC were almost the same.
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Figure 96- PFC and R - PFC compression column specimens
Figure 97 shows the failure pattern of PPFC specimen without and with reinforcement.
For the PFC specimen, initial crack was noticed at 50,000 lbs and specimen split into individual layers. The specimen carried load even after failure and the average maximum load carried by the specimen was about 92,000 lbs. There was no bond between the foamed concrete panel and plain concrete panel within the column specimen. For R –
PPFC specimen, the crack was noticed at the average maximum load i.e. 91,500 lbs.
Crack was noticed at a plain concrete and foamed concrete intersection and had smaller crack width. Under the loading, the specimen acted as a homogeneous unit and did not split into layers due to presence of reinforcement. The loads carried by PPFC and R –
PPFC were almost the same.
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Figure 97- PPFC and R - PPFC compression column specimens
Figure 98 shows the failure pattern of BFC specimen without and with reinforcement. For the BFC specimen, initial crack was noticed at 50,000 lbs and specimen split into individual layers. The specimen carried the load even after failure and the average maximum load carried by the specimen was about 93,000 lbs. There was no bond between the foamed concrete panel and plain concrete panel within the column specimen.
Figure 98- BFC and R -BFC compression column specimens
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For R – BFC specimen, the crack was noticed at maximum load i.e. 91,000 lbs. Crack was noticed at a plain concrete and foamed concrete intersection and had smaller crack width as shown in Figure 98. It was noticed that under the loading, specimen acted as a homogeneous unit and did not split into layers due to the presence of reinforcement. The loads carried by BFC and R – BFC specimens were almost the same.
Figure 99 and Figure 100 show the failure pattern of unreinforced and reinforced Styro,
PFC, PPFC and BFC specimens. It can be clearly seen that specimens with reinforcement had smaller crack width than those specimens without reinforcement. Many hairline cracks were observed in the direction of plane of loading for reinforced column specimen. However fewer cracks were observed for the specimen without reinforcement,
Figure 99- Failure pattern of unreinforced Styro, PFC, PPFC and BFC under compression
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Figure 100- Failure pattern of reinforced Styro, PFC, PPFC and BFC under compression
In the direction of plane of loading, some specimens were noticed to have cracks only on the half portion of the specimen (Figure 101), while for some other specimens, there was a difference in the crack width in the left and right portion of the specimen.
Figure 101- Failure pattern of the specimens due to eccentric loading
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Figure 102 and Figure 103 shows the compressive load vs. strain plot for reinforced and unreinforced Styrofoam, PFC, PPFC and BFC specimens. Among
Styrofoam, PFC, PPFC and BFC, the load carrying capacity for a particular strain is maximum for R - PPFC specimen. Maximum strain carried by the Styro and R – styro specimen was noted to be 0.0007 and 0.0003, PFC and R – PFC specimen was observed to be 0.0003 and 0.0009, for PPFC and R – PPFC specimen it was recorded as 0.0005 and 0.00091. For BFC and R – BFC the maximum strain recorded was 0.0010 and
0.0009. For 0.0006 strains, the maximum compressive load carried by R- styro specimen was 58,000 lbs, R - PFC was 70,000 lbs, R - PPFC it was around 90,000 lbs. For BFC and R – BFC the loads noted were 78,000 lbs and 80,000 lbs respectively. R - PPFC and
R - BFC carrried twice the load carried by Styro specimen.
Compressive - Load vs strain 100000
80000
60000
Load (lb) Load 40000 R-BFC R-PPFC 20000 R-PFC R-styro 0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 Strain
Figure 102- Compressive load vs. strain for reinforced Styrofoam, PFC, PPFC and BFC column specimens
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Compressive - Load vs strain 120000.00
100000.00
80000.00
60000.00
Load (lb) Load BFC 40000.00 PPFC PFC 20000.00 styro 0.00 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 Strain
Figure 103- Compressive load vs. strain for Styrofoam, PFC, PPFC and BFC column specimens
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CHAPTER V
CONCLUSIONS
5.1 Conclusions
After conducting extensive experimental research, the following conclusions were drawn based on the test results from the study:
The optimum mix proportion design for PFC, PPFC and BFC can be
achieved at optimum foam volume of 20 percent and water – cement ratio
of 0.6.
From the mechanical properties such as compressive strength, splitting
tensile strength, modulus of elasticity and poisson’s ratio and flexural
strength of PFC, PPFC and BFC, basalt fiber reinforced (BFC) gives the
maximum compressive strength i.e. 5500 psi. PPFC and PFC gave same
results i.e. 3740 psi. The splitting tensile strength of BFC was noted to be
the maximum i.e. 660 psi. Also, the modulus of elasticity for BFC was
shown maximum among the three types specimens i.e. 1.4 x 106 psi with
poisson’s ratio as 0.21. The flexural strength of BFC of 690 psi was
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recorded highest among all the three groups and is 10 times more than
PFC.
For the reinforced PFC, PPFC and BFC specimen, BFC was observed to
carry maximum load 8000 lbs. and tensile strain 0.0019.
BFC sandwich beam possess highest load carrying capacity (i.e. 18000
lbs) among Styro, PFC, PPFC and BFC specimens.
Steel reinforced PFC compression column specimen carried maximum
load with minimum deflection, among the R – styro, R – PFC, R – PPFC
and R – BFC specimens. On the other hand, R – BFC specimen has the
maximum load carrying capacity with maximum strain under
compression.
Overall, basalt fiber reinforced foamed concrete exhibited all the
characteristics possessed by normal concrete; it can be recommended to be
used in structural application.
5.2 Recommendations
This research study revealed significant potential for structural application of
PFC, PPFC and BFC. It can be used with confidence in future, if following additional studies can be carried out:
The effect of addition of fine aggregate in the design mix proportion on
mechanical properties of PFC, PPFC and BFC need to be studied.
The effect of steel fiber and other types of fiber used in construction
industries on mechanical properties may be studied.
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The properties such as shrinkage, creep and durability, effect of fire on
fiber reinforced foamed concrete and freeze –thaw cycle need to be
investigated.
Further study of bond and the interaction between foamed concrete and
rebar in reinforced PFC, PPFC and BFC is to be studied.
Additionally, in the sandwich beam and column specimens, the bond
between the foamed concrete panel and plain concrete panel need to be
improved in order to achieve better structural performance
The effects of corrosion of steel embedded in foamed concrete over a
period of time need to be investigated.
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APPENDIX
FLOW CHART REPRESENTATION OF EXPERIMENTS
Foamed Concrete
PFC PPFC BFC
Mechanical Properties
Modulus of Reinforced Compressive Splitting Tensile Sandwich Elasticity & Flexural Strength Foamed Strength strength Members Poisson's Ratio Concrete Beams
Compression Sandwich Beams Columns
NC-PFC-NC with without reinforcement reinforcement
NC-PPFC-NC NC-PFC-NC NC-PFC-NC
NC-BFC-NC NC-PPFC-NC NC-PPFC-NC
NC-STYRO-NC NC-BFC-NC NC-BFC-NC
NC-STYRO-NC NC-STYRO-NC
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Trial Mixes
Material and Admixtures
Cement
Ordinary Portland Cement (OPC) of brand CEMEXTM Type-I were used for foam concrete mix.
Fine Aggregate
The fine aggregate was the river sand purchased from the local supplier. The sand was free from clay and impurities. It was dried in an oven for 24 hours and sieved in the sieving machine for #16, #30 and #70 to use in the initial mix design.
Fly ash
Fly ash of class F from the local power plant was used for the foam concrete mix.
Silica Fume
SikaTM brand silica fume were used for the mix.
The other material includes Bentonite and Metakaolin were used, which increased the overall performance of foam concrete.
Fiber
Two types of fibers were used in the mix, polypropylene and basalt (Mini-Bar) fibers.
Water
Tap water supplied in the university was used in this study
Super plasticizer
DURAFLUX 33 normal and high-range water-reducing admixture were used to increase the workability of foam concrete for the initial mix designs.
CATEXOLTM AE 360 air-entraining admixtures were used to create air inside the mix for the later mix designs.
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CATEXOLTM Collaxim L7 viscosity-modifying and SCC stabilizing admixture were for the later mixes to stabilize the ingredient of the foam concrete mix.
Sikament® high-range and mid-range water reducing admixture were replaced with DURAFLUX 33 due to shortage.
Initial Mixing in 5 gal bucket
The materials were weight and were dried-mixed in an empty 5 gallon bucket. On the other hand super plasticizers were mixed in the water. After a uniform dried- mix half of the water were added and mixed until lumps gets scrambled. Foam with certain percentage by volume was added and mixed for some time using mixer – stirrer rod assembly. Later the rest half of the water and fibers for certain mix were added and mixed for 3 minutes. 2 minutes rest was given so as to have reaction of ingredients with water and mixed again for 3 minutes.
Figure 104- Left: Stirrer rod, Right: Foamed concrete mixing in 5 gallon bucket Mix Proportion
Series 1
Mix-I Date of Casting: 01/22/2013
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Table 15- Initial mix proportion
#16 Mix Sand Sand Foam cizers Water Design Cement Volume Sand #30 Sand #70 Sand Bentonite Fly Ash F Superplasti Metakaolin Silica fume (lb) (lb) (lb) (lb) (lb) (lb) (lb) (lb) (ml) (lt) (ft3)
M1 5.86 0.87 2.80 2.80 4.21 7.01 5.53 0.88 20%
M2 5.23 0.87 0.62 2.80 2.80 4.21 7.01 5.53 0.88 20%
M3 4.98 0.25 0.87 0.62 2.80 2.80 4.21 7.01 5.53 0.88 20%
Date of Testing: 01/29/2013
Table 16- Compressive strength for initial mix
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi) 1 85.94 8390 667 2 87.66 4840 385 3 91.10 2820 224 4 96.26 3490 277 5 92.82 2830 225 6 85.94 1850 147 7 101.41 3180 253 8 89.38 3220 256
M3 mix was used for preparing foam concrete specimens. Due to improper mixing of the materials, the samples were scrambled resulting in low compressive strength.
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No inter bond between the materials
Figure 105- Specimen showing improper mixing of the ingredients
Mix-II
Date of Casting: 01/29/2013 water: cementitous material ratio=0.5 Table 17- Mix proportion II
n #16 Mix Sand Sand fume Silica Foam cizers Water Design Cement Sand #30 Sand #70 Sand Bentonite Fly Ash F Metakaoli Superplasti (lb) (lb) (lb) (lb) (lb) (lb) (lb) (lb) (ml) (lb) (ft3) Reduce add d Mix 0.08 4.25 0.21 0.75 0.53 2.39 2.39 3.58 5.97 till 3.9 0 soupy
Date of Testing: 02/05/2013
Table 18- Compressive strength for mix proportion II
Unit Weight Failure Strength # (lb/ft3) Load (lb) (psi) 1 85.94 6180 491 2 85.94 4670 360 3 60.16 690 54 4 60.16 570 45 5 60.16 670 53
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Figure 106- Specimen with slightly higher water - cement ratio
Series 2
Mix-I
Date of Casting: 02/08/2013 w/c ratio= 0.6
Table 19- Modified mix proportion
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers (lb) (lb) (lb) (lb) (gm) (ft3) (lb) 30% by 9.65 1.45 9.65 5.77 82 0.152 vol
Polypropylene Fiber Dosage: 7.5 lb/yd3
Date of Testing: 02/15/13
Table 20- Compressive strength of modified mix proportion
Unit Weight Failure Strength # (lb/ft3) Load (lb) (psi) 1 101.41 21130 1681 2 101.41 22730 1808 3- Fiber 108.29 28600 2275
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Failure Pattern due to presence of fibers
Figure 107- Fiber reinforced foamed concrete
Mix-II
Date of Casting: 03/08/2013 w/c ratio= 0.6
Table 21- Modified mix proportion II
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers (lb) (lb) (lb) (lb) (gm) (ft3) (lb) 20% by 9.65 1.45 9.65 5.77 81.72 0.152 vol.
Polypropylene Fiber Dosage: 7.5 lb/yd3
Date of Testing: 03/15/2013
Table 22- Compressive strength of modified mix proportion II
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi)
1 89.38 27760 2209 2 89.38 28600 2275 3-Fiber 94.54 30050 2391 4-Fiber 94.54 31780 2528
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Figure 108- Failure pattern of PFC Series 3
Mix-I
Date of Casting: 04/04/2013 w/c ratio-0.6, volume of foam- 20%
Table 23- Series 3 initial mix proportion
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers
(lb) (lb) (lb) (lb) (gm) (ft3) (gm) 10.75 1.90 12.65 7.59 91.63 0.068 114.88
Polypropylene Fiber Dosage: 12.11 lb/yd3
Date of Testing: 04/10/2013 *All the specimen contains fiber
Table 24- Compressive strength series 3 initial mix proportion
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi)
1 99.7 30610 2435 2 101.4 32030 2548 3 99.7 32180 2560 4 98.0 29750 2367 5 98.0 31240 2486
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Figure 109- PPFC specimen with 20% foam volume Mix- II
Date of Casting: 04/04/2013 w/c ratio-0.6, volume of foam- 30%
Table 25- Series 3 mix proportion II
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers
(lb) (lb) (lb) (lb) (gm) (ft3) (gm) 10.75 1.90 12.65 7.59 91.63 0.102741 114.88
Polypropylene Fiber Dosage: 12.11 lb/yd3
Date of Testing: 04/10/2013 *All the specimen contains fiber
Table 26- Compressive strength series 3 mix proportion II
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi) 1 96.3 24470 1947 2 96.3 26310 2093 3 96.3 26160 2081 4 96.3 22730 1917 5 99.7 23410 1862
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Figure 110- PPFC specimen with 30 % foam volume
Mix-III:
Date of Casting: 04/04/2013 w/c ratio-0.6, volume of foam- 40%
Table 27- Series 3 mix proportion III
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers
(lb) (lb) (lb) (lb) (gm) (ft3) (gm) 10.75 1.90 12.65 7.59 91.63 0.068 114.88
Polypropylene Fiber Dosage: 12.11 lb/yd3
Date of Testing: 04/10/2013 *All the specimen contains fiber
Table 28- Compressive strength of series 3 mix proportion III
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi) 1 89.4 17410 1385 2 89.4 18210 1449 3 89.4 18160 1445 4 89.4 18070 1437 5 89.4 20590 1638
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Figure 111- PPFC specimen with 40 % foam volume
Mix-IV:
Date of Casting: 05/16/2013 w/c ratio-0.6, volume of foam- 20%
Table 29- Mix proportion for BFC specimen
Silica Fly Super- Cement Water Fiber Foam fume Ash F plasticizers
(lb) (lb) (lb) (lb) (gm) (ft3) (gm) 10.75 1.90 12.65 7.59 91.63 0.103 114.88
Mini-Bar Fiber Dosage: 12.11 lb/yd3
Date of Testing: 05/30/2013 *14- days compressive strength, all the specimen contains fiber
Table 30- Compressive strength of BFC
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi)
1 103.1 56080 4462 2 106.6 59370 4724 3 103.1 57970 4613 4 104.9 57010 4536
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Figure 112- Failure pattern of BFC specimen Series 4
Mix-I:
Date of Casting: 06/07/2013 w/c ratio-0.7, volume of foam- 20%
Table 31- Series 4 mix proportion I
Fly Air Silica Super- Cement Ash Water Fiber Foam VMA Entraining fume plasticizers F Admixture (lb) (lb) (lb) (lb) (gm) (ft3) (ml) (ml) (ml) 10.75 1.90 11.40 7.53 90.00 0.065 35.60 10.7 30.6
1% Polypropylene fiber dosage by volume
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Date of Testing: 06/14/2013 *All the specimen contains fiber
Table 32- Compressive strength series 4 mix proportion I
Unit Weight Failure Load Strength # (lb/ft3) (lb) (psi)
1 94.5 34880 2775 2 94.5 35280 2807 3 96.3 32940 2621 4 96.3 34240 2724 5 96.3 33030 2628
Figure 113- BFC specimen with 1% fiber dosage
Failure Pattern
Figure 114- Failure pattern due to cutting the surface of the specimen
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Table 33- Stress vs. longitudinal strain for PFC
Stress Longitudinal Strain
(psi) (in) 70.70 0.00005 106.06 0.0000875 141.41 0.00011875 176.76 0.00015625
212.12 0.00019375
247.47 0.00023125 282.82 0.00026875 318.18 0.0003 353.53 0.0003375 388.89 0.00036875 424.24 0.0004
459.59 0.00043125 494.94 0.0004625 530.30 0.00049375 565.65 0.000525 601.01 0.00055 636.36 0.00058125 671.71 0.0006125
707.07 0.0006375
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Table 34- Stress vs. longitudinal strain for PPFC specimen
Stress Longitudinal Strain
(psi) (in) 70.61 4.375E-05 105.92 6.875E-05 141.22 0.0000875 176.53 0.0001125 211.84 0.0001375 247.14 0.0001688 282.45 0.0001938 317.76 0.0002188 353.07 0.0002375 388.37 0.0002688 423.68 0.0002875 458.99 0.0003188 494.29 0.0003438 529.60 0.0003688 564.91 0.0003938 600.21 0.0004188 635.52 0.0004375 670.83 0.0004625 706.14 0.0004938
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Table 35- Stress vs. longitudinal strain for BFC
Stress Longitudinal Strain
(psi) (in) 70.61 0.00004375 105.92 0.0000625 141.22 0.0000875 176.53 0.0001125 211.84 0.00013125 247.14 0.00015625 282.45 0.000175 317.76 0.0002 353.06 0.000225 388.37 0.00025 423.68 0.00028125 458.99 0.00030625 494.29 0.00033125 529.60 0.00035625 564.91 0.00038125 600.21 0.00040625 635.52 0.00043125 670.83 0.00045625 706.13 0.00048125 741.44 0.00050625 776.75 0.00053125
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Preparation of Formwork for sandwich panels:
Figure 115- Formwork for sandwich panels and column specimen
Figure 116- Sandwich panels and column specimen after casting
127
Table 36- Analysis of reinforced foamed concrete beam Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 6 in Overall height of beam h 4 in Effective Concrete Cover dc 1 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.22 in Concrete compressive stength f 'c 3500 psi Calculations Effective depth d 3 in Factor β1 β1 0.85 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0122 Balanced reinforcement ratio ρb 0.02494 2 Balanced steel area Asb 0.448982143 in Minimum reinforcement ratio ρmin 0.00333 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.01806 Maximum reinforcement ratio = 0.75ρb 0.01871 governs 2 ACI maximum steel area Asmax 0.32513 in Depth of Neutral Axis - balanced cb 1.77551 Check if the section is over-reinforced Check Under-reinforced Depth of neutral axis c 0.87000 in Depth of the stress block a 0.73950 in Strain in steel εt 0.00734 Factor for over-reinforced section m 34.40435 Ratio of depth of neutral axis to effective depth c/d 0.47144 Check the strain in the steel within the limits check Tension-controlled Nominal moment capacity of the section Mn 2.893 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 2.604 kip-ft
128
PFC Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular
Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 6 in Overall height of beam h 4 in
Effective Concrete Cover dc 1 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.22 in Concrete compressive stength f 'c 3741 psi Calculations Effective depth d 3 in Factor β1 β1 0.85 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0122 Balanced reinforcement ratio ρb 0.02666 2 Balanced steel area Asb 0.47989777 in Minimum reinforcement ratio ρmin 0.00333 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.01931 Maximum reinforcement ratio = 0.75ρb 0.02000 governs 2 ACI maximum steel area Asmax 0.34751 in Depth of Neutral Axis - balanced cb 1.77551 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.81395 in Depth of the stress block a 0.69186 in Strain in steel εt 0.00806 Factor for over-reinforced section m 32.18798 Ratio of depth of neutral axis to effective depth c/d 0.46064 Check the strain in the steel within the Tension- limits check controlled Nominal moment capacity of the section Mn 2.919 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 2.919 kif-ft
129
Total Load 10.010 kip Shear Force 3.303 kip 2 2 Deflection at center, Pa.(3l -4a )/24EIe 0.037 in a 7 inch l 18 inch P 5005 lbs
Ec 1335828.79 psi 4 Ig 32 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 23.90 in Branson's 3 3 4 Ie=[(Mcr/Ma) *Ig]+ [(1-(Mcr/Ma) )*Icr] 23.93 in Equation Mcr 458.73 kip-ft
fr 344.05 psi Ma 2919.48 psi n 21.71 Dead load 41.67 lb Deflection due to dead load = 4 5wl /384EIe 0.00178137
130
PPFC Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular
Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 6 in Overall height of beam h 4 in
Effective Concrete Cover dc 1 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.22 in Concrete compressive stength f 'c 3795 psi Calculations Effective depth d 3 in Factor β1 β1 0.85 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0122 Balanced reinforcement ratio ρb 0.02705 2 Balanced steel area Asb 0.486824923 in Minimum reinforcement ratio ρmin 0.00333 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.01958 Maximum reinforcement ratio = 0.75ρb 0.02028 governs 2 ACI maximum steel area Asmax 0.35253 in Depth of Neutral Axis - balanced cb 1.77551 Check if the section is over-reinforced Check Under- reinforced Depth of neutral axis c 0.80237 in Depth of the stress block a 0.68201 in Strain in steel εt 0.00822 Factor for over-reinforced section m 31.72997 Ratio of depth of neutral axis to effective depth c/d 0.45833 Check the strain in the steel within the limits check Tension- controlled Nominal moment capacity of the section Mn 2.925 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 2.925 kif-ft
131
Total Load 10.028 kip Shear Force 3.327 kip Deflection at center, Pa.(3l2- 2 0.037 4a )/24EIe in a 7 in l 18 in P 5014 lb
Ec 1345435.351 psi 4 Ig 32 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 23.93 in 3 Ie=[(Mcr/Ma) *Ig]+ [(1- Branson's 3 23.97 4 (Mcr/Ma) )*Icr] in Equation Mcr 462.03 kip-ft
fr 346.52 psi Ma 2924.89 kip-ft n 21.55 Dead load 41.67 lb Deflection due to dead load = 4 0.001766232 5wl /384EIe in
132
BFC Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 6 in Overall height of beam h 4 in Effective Concrete Cover dc 1 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.22 in Concrete compressive stength f 'c 4996 psi Calculations Effective depth d 3 in Factor β1 β1 0.8002 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0122 Balanced reinforcement ratio ρb 0.03352 2 Balanced steel area Asb 0.603341328 in Minimum reinforcement ratio ρmin 0.00353 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.02427 Maximum reinforcement ratio = 0.75ρb 0.02514 governs 2 ACI maximum steel area Asmax 0.43690 in Depth of Neutral Axis - balanced cb 1.77551 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.64742 in Depth of the stress block a 0.51806 in Strain in steel εt 0.01090 Factor for over-reinforced section m 25.60232 Ratio of depth of neutral axis to effective depth c/d 0.42440 Tension- Check the strain in the steel within the limits check controlled Nominal moment capacity of the section Mn 3.015 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 3.015 kif-ft
133
Total Load 10.337 Shear Force 3.817 Deflection at center, Pa.(3l2- 2 4a )/24EIe 0.034 a 7 in l 18 in P 5169 lb
Ec 1543718.679 psi 4 Ig 32 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 23.42 in Branson's 3 3 4 Ie=[(Mcr/Ma) *Ig]+ [(1-(Mcr/Ma) )*Icr] 23.46 in Equation Mcr 530.12 kip-ft
fr 397.59 psi Ma 3015.07 kip-ft n 18.79 Dead load 41.67 lb Deflection due to dead load = 4 5wl /384EIe 0.001572381 in
134
Styrofoam Sanwich Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 12 in Overall height of beam h 6 in Effective Concrete Cover dc 1.25 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.33 in Concrete compressive stength f 'c 4693 psi Calculations Effective depth d 4.75 in Factor β1 β1 0.81535 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0058 Balanced reinforcement ratio ρb 0.03208 2 Balanced steel area Asb 1.828685741 in Minimum reinforcement ratio ρmin 0.00343 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.02323 Maximum reinforcement ratio = 0.75ρb 0.02406 governs 2 ACI maximum steel area Asmax 1.32422 in Depth of Neutral Axis - balanced cb 2.81122 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.50731 in Depth of the stress block a 0.41363 in Strain in steel εt 0.02509 Factor for over-reinforced section m 26.74889 Ratio of depth of neutral axis to effective depth c/d 0.32364 Check the strain in the steel within the Tension- limits check controlled Nominal moment capacity of the section Mn 7.496 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 7.496 kif-ft
135
Total Load 12.851 kip 2 2 Deflection at center, Pa.(3l -4a )/24EIe 0.063 in a 14 inch l 32 inch P 6425 kips
Ec 3114852 psi 4 Ig 208 in 3 2 4 Icr=(b.c /3) + (d-c) * (n*As) 55.83 in 4 B ranson's 3 3 in Ie=[(Mcr/Ma) *Ig]+ [(1-(Mcr/Ma) )*Icr] 59.81 Equation Mcr 2226.43 kip-ft
fr 385.34 psi
Ma 7496.25 psi
n 9.31 Dead load 225.00 lb Deflection due to dead load = 4 5wl /384EIe 0.01648869
136
PFC Sanwich Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 12 in Overall height of beam h 6 in Effective Concrete Cover dc 1.25 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.33 in Concrete compressive stength f 'c 5507 psi Calculations Effective depth d 4.75 in Factor β1 β1 0.77465 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0058 Balanced reinforcement ratio ρb 0.03577 2 Balanced steel area Asb 2.038755054 in Minimum reinforcement ratio ρmin 0.00371 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.02590 Maximum reinforcement ratio = 0.75ρb 0.02683 governs 2 ACI maximum steel area Asmax 1.47634 in Depth of Neutral Axis - balanced cb 2.81122 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.45503 in Depth of the stress block a 0.35249 in Strain in steel εt 0.02832 Factor for over-reinforced section m 23.99273 Ratio of depth of neutral axis to effective depth c/d 0.30966 Check the strain in the steel within the Tension- limits check controlled Nominal moment capacity of the section Mn 7.547 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 7.547 kif-ft
137
Total Load 12.937 kip Shear Strength 6345 lb Deflection at center, Pa.(3l2- 2 4a )/24EIe 0.059 in a 14 inch l 32 inch P 6469 lbs
Ec 3374191 psi 4 Ig 216 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 52.70 in 3 Ie=[(Mcr/Ma) *Ig]+ [(1- Branson's 3 4 (Mcr/Ma) )*Icr] 58.67 in Equation Mcr 2504.56 kip-ft
fr 417.43 psi
Ma 7546.69 psi n 8.59 Dead load 225.00 lb Deflection due to dead load = 4 5wl /384EIe 0.015519 in
138
PPFC Sanwich Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 12 in Overall height of beam h 6 in Effective Concrete Cover dc 1.25 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.33 in Concrete compressive stength f 'c 6745 psi Calculations Effective depth d 4.75 in Factor β1 β1 0.71275 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0058 Balanced reinforcement ratio ρb 0.04031 2 Balanced steel area Asb 2.297542898 in Minimum reinforcement ratio ρmin 0.00411 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.02919 Maximum reinforcement ratio = 0.75ρb 0.03023 governs 2 ACI maximum steel area Asmax 1.66374 in Depth of Neutral Axis - balanced cb 2.81122 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.40378 in Depth of the stress block a 0.28779 in Strain in steel εt 0.03229 Factor for over-reinforced section m 21.29027 Ratio of depth of neutral axis to effective depth c/d 0.29482 Check the strain in the steel within the Tension- limits check controlled Nominal moment capacity of the section Mn 7.600 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 7.600 kif-ft
139
Total Load 13.029 kip 2 2 Deflection at center, Pa.(3l -4a )/24EIe 0.062 in a 14 inch l 32 inch P 6514 kips
Ec 1793692 psi 4 Ig 216 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 101.05 in Branson's 3 3 4 Ie=[(Mcr/Ma) *Ig]+ [(1-(Mcr/Ma) )*Icr] 106.62 in Equation Mcr 2771.82 kip-ft
fr 461.97 psi
Ma 7600.07 psi n 16.17 Dead load 225.00 lb Deflection due to dead load = 4 5wl /384EIe 0.0160629 in
140
BFC Sanwich Beam: Analysis of singly reinforced concrete beam Valid for under-reinforced, balanced and over-reinforced beams
Assumption Type of beam Rectangular Crushing strain of concrete εcu 0.003 in/in Single layer of bars Normal weight concrete Modulus Elasticiy of Steel E 29000000 psi Data Width of the beam b 12 in Overall height of beam h 6 in Effective Concrete Cover dc 1.25 in Tensile strength of steel bars fy 60000 psi 2 Total area of steel bars As 0.33 in Concrete compressive stength f 'c 6993 psi Calculations Effective depth d 4.75 in Factor β1 β1 0.70035 Yield strain for steel εy 0.00207 in/in Steel reiforcement ratio ρ 0.0058 Balanced reinforcement ratio ρb 0.04106 2 Balanced steel area Asb 2.340577954 in Minimum reinforcement ratio ρmin 0.00418 governs Minimum reinforcement ratio 0.00333 Maximum reinforcement ratio with εt > 0004 ρmax 0.02974 Maximum reinforcement ratio = 0.75ρb 0.03080 governs 2 ACI maximum steel area Asmax 1.69490 in Depth of Neutral Axis - balanced cb 2.81122 Under- Check if the section is over-reinforced Check reinforced Depth of neutral axis c 0.39636 in Depth of the stress block a 0.27759 in Strain in steel εt 0.03295 Factor for over-reinforced section m 20.89882 Ratio of depth of neutral axis to effective depth c/d 0.29257 Check the strain in the steel within the Tension- limits check controlled Nominal moment capacity of the section Mn 7.608 kip-ft Strength reduction for the flexure ɸ 0.900 Design moment capacity ɸMn 7.608 kif-ft
141
Total Load 13.043 kip 2 2 Deflection at center, Pa.(3l -4a )/24EIe 0.061 in a 14 inch l 32 inch P 6522 kips
Ec 1826370 psi 4 Ig 216 in 2 2 4 Icr=(b.c /2) + (d-c) * (n*As) 99.57 in Branson's 3 3 4 Ie=[(Mcr/Ma) *Ig]+ [(1-(Mcr/Ma) )*Icr] 105.51 in Equation Mcr 2822.32 kip-ft
fr 470.39 psi
Ma 7608.49 psi n 15.88 Dead load 225.00 lb Deflection due to dead load = 4 5wl /384EIe 0.015942 in.
Calculation of maximum load for column specimen:
Ag 36 in 2 f'c (psi) Ast 0.44 in2 Styro 4693 fy 60000 psi PFC 5507 Pn=0.85 F'c(Ag-Ast)+fyAst reinforced PPFC 6745 Pn=0.85 F'c(Ag-Ast) unreinforced BFC 6993
Maximum Load
Specimen Unreinforced Reinforced Type Specimen (kips) Specimen (kips) Styro 130 154 PFC 153 177 PPFC 187 211 BFC 194 218
142