CHAPTER 1

INTRODUCTION

1.1 GENERAL

Concrete is probably the most widely used man-made construction material in the

world. Concrete is second highest consumptive material after water, which is used world

wide for most of the constructions. The properties of concrete, which makes it suitable

material for construction purpose, are high compressive strength, wear and tear

resistance, durability, excellent bonding, economy etc.

Concrete and steel were always considered the most important, and the most

commonly used structural materials. The development of new high-performance

composite materials that are stronger and more durable than conventional materials (e.g.,

Portland cement concrete, steel, wood, and masonry) is important to the construction

industry.

In spite of this, it has some serious deficiencies; it is inherently weak in tensile

strength compared to other construction materials, a low specific modulus, limited

ductility, and little resistance to cracking.

Conventional concrete is very weak in tension; its tensile strength is only 10% of

its compressive strength so here is an attempt made to improve tensile strength by the

incorporation of Carbon Fibers, which is a nano material. Carbon fiber is an important

development in the field of concrete technology. Available literature is an indicator to

the tremendous interest and enthusiasm shown in adoption of carbon fiber for

construction.

CHAPTER 2

REVIEW OF LITERATURE

2.1 HISTORY OF CARBON FIBERS

In 1958, Dr. Roger Bacon created the first high-performance carbon fibers at the

Union Carbide Parma Technical Center, located outside of Cleveland, Ohio.[The first

fibers were manufactured by heating strands of rayon until they carbonized. This process

proved to be inefficient, as the resulting fibers contained only about 20% carbon and had

low strength and stiffness properties. In the early 1960s, a process was developed using

polyacrylonitrile (PAN) as a raw material. This had produced a carbon fiber that

contained about 55% carbon and had much better properties. The polyacrylonitrile (PAN)

conversion process quickly became the primary method for producing carbon fibers. The

high potential strength of carbon fiber was first realized in 1963 in a process developed at

the Royal Aircraft Establishment at Farnborough in the UK.

CHAPTER 3

CARBON FIBER

4.1 Concept of Carbon Fiber

Carbon fiber is a polymer, which is a form of graphite. Graphite is a form of pure

carbon. In graphite the carbon atoms are arranged into big sheets of hexagonal aromatic

rings. The sheets look like chicken wire.( Fig 4) Carbon fiber is a form of graphite in

which these sheets are long and thin.

Fig 4

Carbon Fiber is a material consisting of extremely thin fibers about 0.005–0.010

mm in diameter and composed mostly of carbon atoms. The carbon atoms are bonded

together in microscopic crystals that are more or less aligned parallel to the long axis of

the fiber. Fig 5 shows a comparison of carbon fiber to human hair. Carbon filament can

be as seen in Fig 6.

Fig 5 A 6μm diameter carbon filament compared to a human hair

Fig 6 Carbon Fiber Filament

The crystal alignment makes the fiber very strong for its size. Several thousand

carbon fibers are twisted together to form a yarn, which may be used by itself or woven

into a fabric.(Fig 7) The density of carbon fiber is also considerably lower than the

density of steel, making it ideal for applications requiring low weight.

The properties of carbon fiber such as high tensile strength, low weight, and low

thermal expansion make it very popular in aerospace, civil engineering, military, and

motorsports, along with other competition sports. The properties of carbon fiber such as

high tensile strength, low weight, and low thermal expansion make it very popular in

aerospace, military, and motorsports along with other competition sports. The unique

appearance of carbon fiber also makes it popular for stylistic purposes.

Carbon fibers are used in concrete for increasing the tensile and flexural

strengths,increasing the tensile ductility and flexural toughness,decreasing the drying

shrinkage and rendering the concrete the ability to sense its own strain.

Fig 7 Carbon Fabric

4.2 Why carbon fiber?

Carbon fiber has a remarkably high strength and light weight compared to other traditional materials.

It can be produced with very high modulus for applications such as spacecraft, arms etc.

It is flexible in structural design

It has chemical resistivity and non corrosiveness properties.

It has good properties thermal and electric conductivity.

4.2.1 Carbon fiber reinforcements have several distinct advantages over

traditional types of reinforcement. Listed below are some of its

advantages

Lightweight

Non-corrosive

Alkali resistant

Easy to handle and install

Low aesthetic impact

Flexible and can be wrapped around complex shapes

Acid resistant

Very high-strength & high modulus of elasticity

Outstanding fatigue resistance

4.3 APPLICATION OF CARBON FIBER

Strengthening of columns for enhancing load carrying capacity.

Strengthening of beams for enhanced flexure and shear strengths.

Strengthening of slabs, retaining walls etc.

Strengthening of bridge piers, jetty piles etc for earthquake resistance.

Improvement of impact and blast resistant properties.

Act as barrier to Carbon dioxide, chloride, sulphate etc for RC structures.

4.4 ADVANTAGES

Very high strength to thickness or weight ratio - Appreciable

increase in strength and load carrying capacity without significant increase in

dead load.

Enhanced stiffness, shear and tensile capacity - Increased load carrying

capacity and better resistance to seismic forces and deflection.

Chemical resistant - Excellent resistance to acids and alkalies.

Flexible - Can be applied to any shape.

Thin sections -Can be effectively used in space-constrained areas.

Creep and Fatigue resistance -Ideal for conditions of sustained loading and

repeated loading.

Economical -easy to install, time and labour saving.

4.5 THE EFFECT OF CARBON FIBERS ON THE

PROPERTIES OF CONCRETE

Increased flexural strength

Increased flexural toughness

Increased durability under cyclic loading

Decreased compressive strength

Increased air content

Improved freeze thaw durability

Decreased drying shrinkage

Decreased electrical resistivity

Increased electromagnetic interference shielding effectiveness

Increased thermal conductivity

Improved resistance to earthquake damage

4.6 SYNTHESIS OF CARBON FIBERS

Fig 8. Synthesis of carbon fiber

Carbon fiber is produced by pyrolysis of an organic precursor fiber in an inert

atmosphere at temperatures above 982°C/1800°F.There are various stages in the

synthesis of carbon fibers.These are polymerization and spinning, oxidation (also referred

to as stabilization), carbonization (sometimes inaccurately referred to as graphitization),

surface treatment and sizing application.

Polymerization

The process begins with a polymeric feedstock known as a precursor (“that which

comes before”), which provides the fiber’s molecular backbone. Today about 10 percent

of produced carbon fiber is made from a rayon- or pitch-based precursor, but the majority

is derived from polyacrylonitrile (PAN), made from acrylonitrile, which is derived from

the commodity chemicals propylene and ammonia.

Production of PAN-based carbon fiber

Most of a carbon fiber producer’s investment is spent on precursor, and the quality of the

finished fiber is directly dependent on that of the precursor.

Precursor formulation begins with an acrylonitrile monomer, which is combined

in a reactor with plasticized acrylic comonomers and a catalyst, such as sulfur dioxide

acid or sulfuric acid. Continuous stirring blends the ingredients, ensures consistency and

purity and initiates the formation of free radicals within the acrylonitrile’s molecular

structure. This change leads to polymerization, the chemical process that creates long-

chain polymers that can be formed into acrylic fibers.

After washing and drying, the acrylonitrile, now in powder form, is dissolved in

either organic solvents, such as dimethyl sulfoxide (DMSO), dimethyl acetamide

(DMAC) or dimethyl formamide (DMF), or aqueous solvents, such as zinc chloride and

rhodan salt. Organic solvents help avoid contamination by trace metal ions that could

upset thermal oxidative stability during processing and retard high-temperature

performance in the finished fiber. At this stage, the powder-and-solvent slurry, or

precursor “dope,” is the consistency of maple syrup.

Spinning

PAN fibers are formed by a process called wet spinning. The dope is immersed in

a liquid coagulation bath and extruded through holes in a spinneret made from precious

metals. The spinneret holes match the desired filament count of the PAN fiber (e.g.,

12,000 holes for 12K carbon fiber). This wet-spun fiber, relatively gelatinous and fragile,

is drawn by rollers through a wash to remove excess coagulant, then dried and stretched

to continue the orienting of the PAN polymer. Here, the filament’s external shape and

internal cross-section are determined by the degree to which the selected solvent and

coagulant have penetrated the precursor fiber, the amount of applied tension and the

percentage of filament elongation. The last step in PAN precursor fiber formation is the

application of a finishing oil to prevent the tacky filaments from clumping. The white

PAN fiber then is dried again and wound onto bobbins.

Oxidation

These bobbins are loaded into a creel that feeds the PAN fiber through a series of

specialized ovens during the most time-consuming stage of production, oxidation. Before

they enter the first oven, the PAN fibers are spread flat into a tow band or sheet referred

to as warp. The oxidation oven temperature ranges from 392°F to 572°F (200°C to

300°C). The process combines oxygen molecules from the air with the PAN fibers in the

warp and causes the polymer chains to start crosslinking. This increases the fiber density

from ~1.18 g/cc to as high as 1.38 g/cc.

To avoid runaway exotherm (the total exothermic energy released during

oxidation) oven manufacturers use a variety of airflow designs to help dissipate heat and

control temperature. Oxidation time varies, driven by specific precursor chemistry. An

elapsed time of 60 to 120 minutes is typical, as are four to six ovens per production line,

with ovens stacked to provide two heating zones that offer 11 to 12 passes of the fiber per

oven. In the end, the oxidized (stabilized) PAN fiber contains about 50 to 65 percent

carbon molecules, with the balance a mixture of hydrogen, nitrogen and oxygen.

Carbonization

Carbonization occurs in an inert (oxygen-free) atmosphere inside a series of specially

designed furnaces that progressively increase the processing temperatures. At the

entrance and exit of each furnace, purge chambers prevent oxygen intrusion because

every oxygen molecule that is carried through the oven removes a portion of the fiber. In

the absence of oxygen, only noncarbon molecules, including hydrogen cyanide elements

and other VOCs (generated during stabilization ) and particulate (such as local buildup of

fiber debris), are removed and exhausted from the oven for post-treatment in an en-

vironmentally controlled incinerator. carbonization begins in a low-temperature furnace

that subjects the fiber to 1292°F to 1472°F (700°C to 800°C) and ends in a high-

temperature furnace at 2192°F to 2732°F (1200°C to 1500°C). Fiber tensioning must be

continued throughout the production process. Ultimately, crystallization of carbon

molecules can be optimized to produce a finished fiber that is more than 90 percent

carbon. Although the terms carbon and graphite are often used interchangeably, the

former denotes fibers carbonized at about 1315°C/2400°F and that contain 93 to 95

percent carbon. The latter are graphitized at 1900°C to 2480°C (3450°F to 4500°F) and

contain more than 99 percent elemental carbon. As the fiber is carbonized, it loses weight

and volume, contracts by 5 to 10 percent in length and shrinks in diameter.

Surface treatment and sizing

The next step is critical to fiber performance and, apart from the precursor, it most

differentiates one supplier’s product from its competitors’ product. Surface treatment and

sizing increase the fiber’s total surface area and porosity. Adhesion between matrix resin

and carbon fiber is crucial in a reinforced composite; during the manufacture of carbon

fiber, surface treatment is performed to enhance this adhesion. Producers use different

treatments, but a common method involves pulling the fiber through an electrochemical

or electrolytic bath that contains solutions, such as sodium hypochlorite or nitric acid.

These materials etch or roughen the surface of each filament, which increases the surface

area available for interfacial fiber/matrix bonding and adds reactive chemical groups,

such as carboxylic acids. Next, a highly proprietary coating, called sizing, is applied. At

0.5 to 5 percent of the weight of the carbon fiber, sizing protects the carbon fiber during

handling and processing (e.g., weaving) into intermediate forms, such as dry fabric.

Sizing also holds filaments together in individual tows to reduce fuzz, improve

processability and increase interfacial shear strength between the fiber and matrix resin.

CHAPTER 4

CONCEPT OF INVESTIGATION

5.1 COMPOSITE MATERIALS

Composite materials (or composites for short) are engineered materials made

from two or more constituent materials with significantly different physical or chemical

properties which remain separate and distinct on a macroscopic level within the finished

structure.

The most primitive composite materials were straw and mud combined to form

bricks for building construction. Composites are made up of individual materials referred

to as constituent materials. There are two categories of constituent materials: matrix and

reinforcement. At least one portion of each type is required. The matrix material

surrounds and supports the reinforcement materials by maintaining their relative

positions. The reinforcements impart their special mechanical and physical properties to

enhance the matrix properties. The matrix material can be introduced to the

reinforcement before or after the reinforcement material is placed into the mold cavity or

onto the mold surface. Most commercially produced composites use a polymer matrix

material often called a resin solution. There are many different polymers available

depending upon the starting raw ingredients . The most common are known as polyester ,

vinyl ester, epoxy, phenolic, polyimide, polyamide, polypropylene, PEEK, and others.

The reinforcement materials are often fibers but also commonly ground minerals.

Products :

Composite materials have gained popularity (despite their generally high cost) in high-

performance products that need to be lightweight, yet strong enough to take harsh loading

conditions such as aerospace components (tails, wings, fuselages, propellers), boat,

bicycle frames and racing car bodies.

5.1.1 FIBERS

Fibers are special case of reinforcements. They are generally continuous and have

diameter from 3 to 200 μm. Fibers are linear elastic or perfectly plastic. Fibers are

generally stiffer and stronger than same material in bulk form.

5.1.2 MATRIX

Matrix is binder material that supports, separates and protects the fibers. It

provides a path by which load is transferred to the fibers and redistributed among the

fibers in the event of fiber breakage. Matrix has lower density, stiffness and strength than

the fibers. Matrix material must be capable of being poured around the reinforcement

during some stage in manufacture of composites.

5.2 ORIENTATION OF FIBERS

More random the orientation, more fibers are needed to resist the load that is

because only the smaller fraction of randomly oriented fibers are oriented in right

direction.

Three levels of reinforcing in concrete –

Random 3D reinforcing – This occurs when fibers are mixed into concrete and

poured into forms. The fibers are distributed evenly in concrete and point in all different

directions. Very few fibers actually are able to resist the tensile loads in the specific

direction. This level of fiber reinforcing is inefficient requiring very high loads of fibers.

1D reinforcing is very efficient because it requires least amount of material to

resist the tensile loads. Reinforcing is placed entirely in the tension zone thereby

maximizing the effectiveness without wasting reinforcement in area that does not

generate tensile loads.

CHAPTER 5

EXPERIMENTAL INVESTIGATIONS

6.1 EXPERIMENTAL PROGRAMME

The investigation aims at comparing the flexural strength of plain concrete with

carbon fiber based concrete in which carbon fibers have different orientations.

Specific gravity, water absorption and sieve analysis of coarse and fine aggregates

is found out. Specific gravity of cement is found out.

Concrete mix is designed with the physical properties of available materials for

M20 concrete by using IS 10262:1982.

Experiments have been carried out for the following types of concrete

Plain Concrete

Concrete with carbon fibers in different orientations

Different orientations of fibers in the concretes tested are as shown in Fig 9.

In case of random distribution of fibers, Carbon fibers with the quantity of 2% of

the volume of cement are added.

In case of layered distribution, fibers are cut to the dimensions of the mould and

distributed in the form of layers.

For determining the flexural strength beam specimen of dimensions 100mm x

100mm x 500mm are cast and tested under central single point loading as per IS

516:1959.

Also comparison of test results is made to find variation in flexural strength

between concrete with random fiber distribution and concrete with layered

distribution.

Fig 9. Different orientations of carbon fibers in concretes tested.

6.2 MATERIALS

6.2.1 Materials used in the experimentation

Ordinary Portland Cement of 43 Grade

Coarse aggregates of 10 mm and down size

Fine aggregates

Carbon Fibers

Carbon Fiber cut into pieces 10mm length Dry mix

Casting of beams

Testing of beams in UTM under Single point load

6.2.2 Properties tested of the materials used in the experimentation

Ordinary Portland Cement

SPECIFIC GRAVITY = 3.212

Coarse Aggregates

SPECIFIC GRAVITY = 2.6

SIEVE ANALYSIS

Fineness modulus = 5.885

Fine Aggregates

SPECIFIC GRAVITY = 2.546

WATER ABSORPTION = 1.14%

SIEVE ANALYSIS Fineness modulus = 2.646

Carbon Fibers

Properties:

Fiber orientation Unidirectional

Weight of fiber 200 g/m2

Density of fiber 1.80 g/cc

Fiber thickness 3 mm

Ultimate elongation (%) 1.5

Tensile strength 3500 N/mm2

Tensile modulus 285 x 103 N/mm2

6.3 CONCRETE MIX DESIGN

(a) Design stipulations

1. Characteristic compressive strength required in the field days – 20 MPa

2. Maximum size of aggregates used in the concrete mix – 10 mm

3. Degree of workability of the concrete mix – 0.90

4. Degree of quality control – GOOD

5. Type of exposure – MILD

(b) Test Data of the Materials

1. Specific gravity of cement: 3.21

2. Specific gravity of coarse aggregates: 2.6

3. Specific gravity of fine aggregates: 2.55

4. Water absorption:

Coarse aggregates: 0.5%

Fine aggregates: 1.15%

5. Free (surface) moisture

Coarse aggregates: NIL

Fine aggregates: 2%

(c) Target mean strength of concrete

Target mean strength of concrete for specified characteristic cube strength in fck:

20 + ( t x s)

where, t = 1.65 and s = 4

20 + ( 1.65 x 4)

= 26.6 MPa

(Refer Table 11.21 and Table 11.22 for values of t and s)

(d) Selection of water cement ratio

From fig 11.10 the water cement ratio required for the target mean strength of

26.6 MPa is 0.5. This is lower than the maximum value of 0.55 prescribed

for mild exposure (refer Table 9.18). Adopt water cement ratio of 0.5.

(e) Selection of water and sand content

From Table 11.24 for 10mm maximum size aggregate, sand conforming to grading

Zone II, water content per cubic meter of concrete = 20 kg and sand content as % of

total aggregate by absolute volume = 40%. For change in value of water cement ratio,

Compacting factor for sand belonging to Zone III following adjustment is required.

Required sand cement content as % of total aggregate by absolute volume

40 – 1.5 = 38.5

Required water content = 200 + 0 = 200 l/m3

(f) Determination of cement content

Water cement ratio = 0.50

Water = 200 liters

Cement = 200/ 0.50 = 400 kg/ m3

This cement content is adequate for mild exposure condition.

(Refer Table 19.8)

(g) Determination of coarse aggregate and fine aggregate content

From Table 11.23 for specified maximum size of aggregate of 10 mm the amount of

Entrapped air in the wet concrete is 3%

Taking this into account and applying equations 1 and 2

Where, V = Absolute volume of fresh concrete, which is equal to gross volume

minus the volume of entrapped air.

w = Water content

C = Cement content

Sc = Specific gravity of cement

P = Ratio of FA to total aggregate by absolute volume

Fa = fine aggregate content

Sfa = Specific gravity of fine aggregate

fa = 634 Kg / m3

Ca = 1033 Kg / m3

The mix proportion then becomes

Water 200 liters/ m3

Cement 400 Kg/ m3

Fine aggregates 634 Kg/ m3

Coarse aggregates 1033 Kg/ m3

The ratio is found out to be 1: 1.585: 2.580

6.4 TESTING PARAMETER

Modulus of Rupture

In flexural loading test 50x10x10 cm concrete beam is loaded at a rate of 0.8 to

1.2Mpa /min. Flexural strength is expressed in terms of modulus of rupture ,which is the

maximum stress at rupture computed from the flexural formula,

R = PL BD2

Where, R= Modulus of rupture

P = Maximum load

L = Span length

B = Width

D = Depth of the section

The above formula is valid only if the fracture in the tension surface is within the

middle third of the span length (i.e. a > 13.3cm).

When the fracture is outside by more than 5% of the span length (i.e. a < 11cm),

then the test results are rejected.

If the fracture is outside by not more than 5% of the span length, a modified

formula is used:

R= 3Pa BD2

Where, a = The average distance between the line of fracture and the nearest support

measured on the tension surface of the beam.

6.5 CALCULATION OF QUANTITY OF MATERIALS FOR

ONE BEAM

1. Plain concrete without carbon fibers

Mix arrived= 1:1.585:2.580

Volume of one beam= 0.1*0.1*0.5=0.005m3

Weight of concrete= 12 Kg

Weight of cement= 12/ (1+1.585+2.580) = 2.32 Kg

Weight of sand = (2.32*1.585) = 3.677 Kg

Weight of aggregates= (2.32*2.580) = 5.985 Kg

2. Random distribution:

Mix arrived= 1:1.585:2.580

Volume of one beam= 0.1*0.1*0.5=0.005m3

Weight of concrete= 12 Kg

Weight of cement= 12/ (1+1.585+2.580) = 2.32 Kg

Weight of sand = (2.32*1.585) = 3.677 Kg

Weight of aggregates= (2.32*2.580) = 5.985 Kg

Carbon fiber content= 2% of cement

= (2/100)*2.32= 0.046 Kgs = 46.4 gms =0.232 m2

3. Layered distribution (4 layers):

Mix arrived= 1:1.585:2.580

Volume of one beam= 0.1*0.1*0.5=0.005m3

Weight of concrete= 12 Kg

Weight of cement= 12/ (1+1.585+2.580) = 2.32 Kg

Weight of sand = (2.32*1.585) = 3.677 Kg

Weight of aggregates= (2.32*2.580) = 5.985 Kg

Carbon fiber content for one layer =0.1*0.5=0.5 m2

For four layers= 0.5*4= 0.2 m2= 44.8 gms

4. Alternate PC layer and random distribution layer (3 PC layers and 2 random

distribution concrete layers)

Total quantity of material for PC layers:

Volume of one layer of concrete = (0.1*0.5*0.02) = 0.001 m3

Volume of 3 layer of plain concrete = (3*0.001) = 0.003 m3

Weight of concrete = (0.003*2400) =7.2 Kgs

Weight of cement = (7.2/ (1+1.585+2.580)) = 1.390 Kg

Weight of sand = (1.390*1.585) = 2.203 Kg

Weight of aggregates = (1.390*2.580) = 3.586 Kg

Total quantity of material for random distribution concrete layers:

Volume of 2 layers = (2*0.001) = 0.002 m3

Weight of concrete = (0.002*2400) = 4.8 Kg

Weight of cement = (4.8/ (1+1.585+2.580)) = 0.930Kg

Weight of sand = (0.930*1.585) = 1.474Kg

Weight of aggregates = (0.930*2.580) = 2.399 Kg

Carbon fiber content for two layers of random distribution = 2% of cement

= (2/100)*0.93 = 18.00 gms

= (18.96/200) = 0.090 m2

5. Alternate PC layer and random distribution layer with intermediate carbon fiber

layer(3 PC layers and 2 random distribution concrete layers and 2 carbon fiber

layers)

Total quantity of material for PC layers:

Volume of one layer of concrete = (0.1*0.5*0.02) = 0.001 m3

Volume of 3 layer of plain concrete = (3*0.001) = 0.003 m3

Weight of concrete = (0.003*2400) =7.2 Kgs

Weight of cement = (7.2/ (1+1.585+2.580)) = 1.390 Kg

Weight of sand = (1.390*1.585) = 2.203 Kg

Weight of aggregates = (1.390*2.580) = 3.586 Kg

Total quantity of material for random distribution concrete layers:

Volume of 2 layers = (2*0.001) = 0.002 m3

Weight of concrete = (0.002*2400) = 4.8 Kg

Weight of cement = (4.8/ (1+1.585:2.580)) = 0.930Kg

Weight of sand = (0.930*1.585) = 1.474Kg

Weight of aggregates = (0.930*2.580) = 2.399 Kg

Carbon fiber content for two layers of random distribution = 2% of cement

= (2/100)*0.930 = 18.60 gms

= (18.60/200) = 0.0948 m2

Carbon fiber content for 2 layers = ( 0.1*0.5)*2 =0.1 m2

Total fiber content =0.0948 + 0.1 =0.193 m2 =38.60 gm

CHAPTER 6

RESULTS

7.1.1 Plain concrete

Specimen 1 Ultimate load =27KN

Distance of crack from nearest support = a = 16.5 cm

Maximum displacement =2.6 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (27*103*400)/ (100*1002)

=10.8 N/mm2

Specimen 2

Ultimate load =28KN

Distance of crack from nearest support = a = 18.5cm

Maximum displacement = 2.3 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (28*103*400)/ (100*1002)

= 11.2 N/mm2

Mean modulus of rupture for plain concrete -11 N/mm2

7.1.2 Layered distribution

Specimen 1 Ultimate load =23 KN

Distance of crack from nearest support = a = 17.5 cm

Maximum displacement =0.9 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (23*103*400)/ (100*1002)

= 9.2 N/mm2

Specimen 2 Ultimate load =24 KN

Distance of crack from nearest support = a = 19.5 cm

Maximum displacement =1.2 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (24*103*400)/ (100*1002)

= 9.6 N/mm2

Mean R = 9.4 N/mm2

7.1.3. Random Distribution

Specimen 1

Ultimate load =28 KN

Distance of crack from nearest support = a = 15 cm

Maximum displacement =2 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (28*103*400)/ (100*1002)

= 11.2 N/mm2

7.1.4 Alternate PC layer and Random distribution layer

Specimen 1

Ultimate load =29 KN

Distance of crack from nearest support = a = 18.5 cm

Maximum displacement =2 mm

Modulus of rupture =R = (P*L)/ (B*D2)

= (29*103*400)/ (100*1002)

= 11.6 N/mm2

Specimen 2

Ultimate load =30 KN

Distance of crack from nearest support = a = 18 cm

Maximum displacement =3.6 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (30*103*400)/ (100*1002)

= 12 N/mm2

Mean R= 11.6 N/mm2

7.1.5 Alternate PC layer and Random CF concrete layer with intermediate carbon fiber layer:

Specimen 1

Ultimate load =30 KN

Distance of crack from nearest support = a = 21 cm

Maximum displacement =0.5 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (30*103*400)/ (100*1002)

= 12 N/mm2

Specimen 2

Ultimate load =29 KN

Distance of crack from nearest support = a = 20.5 cm

Maximum displacement =0.3 mm

Modulus of rupture =R= (P*L)/ (B*D2)

= (29 *103*400)/ (100*1002)

= 11.6 N/mm2

Mean R= 11.8 N/mm2