BEHAVIOUR OF HIGH STRENGTH REINFORCED
CONCRETE BEAM WITH METAKAOLIN UNDER
STATIC LOADING
AMER BIN YUSUFF @ MD YUSOFF
UNIVERSITI TEKNOLOGI MALAYSIA
BEHAVIOUR OF HIGH STRENGTH REINFORCED CONCRETE BEAM
WITH METAKAOLIN UNDER STATIC LOADING
AMER B YUSUFF @ MD YUSOFF
A project report submitted in partial fulfilment of the
requirements for the award of the degree of
Master of Engineering (Civil-Structure)
Faculty of Civil Engineering
Universiti Teknologi Malaysia
APRIL 2005
iii
To my mother Arison bt Haron and late father Yusuff @ Md Yusoff bin Puteh
for your companionship, understanding and
continuous encouragement over the years.
iv
ACKNOWLEDGEMENT
The name of Allah, the most Gracious, the Dispenser of Grace, Salam to
Nabi Muhammad SAW. His companion and friends as well to all the people who
follow his path.
I would like to express my highest appreciation to my supervisor Assoc
Prof Dr Abd Latif Saleh for his advice and guidance during the course of this
project. His invaluable assistance and the constructive criticisms offered have
resulted in the completion of this project.
Unforgettable, I would like to thank to Laboratory Technicians and
research assistance of Civil Engineering Faculty, UiTM Penang for their kind
help in assisting my project.
Last but not least, I would like to express special gratitude to my family,
Khalilah Adibah Muhammad, Aiman Haziq, Aina Hazwani and Aimi Batrishiya
for their persistent support in my studying at UTM. Also to my colleagues, your
helps are really appreciated and will be remembered forever
v
ABSTRACT
The need of cement replacement material (CRM) in reinforced concrete has
gained its popularity among the researchers to produce a high strength concrete
(HSC) for structural engineering application. This paper presents the experimental
results of the static loading effect on reinforced concrete beam with metakaolin
(MK7003). Three different percentages, 5%, 10% and 15% of MK7003 were
incorporated as CRM in reinforced concrete beam, and 0% of MK7003 as the
control specimen. Eight no of beams, with dimension of 1400mm x 150mm x
125mm, were tested, two for each different percentages and two beams as control
specimens. The beams were subjected to four point loading test until failure. The
findings of the experiment been shown that the structural performance were
improved with the inclusion of MK7003. The observation made suggested that
MK7003 with 10% replacement gave the optimum performance of the reinforced
concrete.
vi
ABSTRAK
Keperluan bahan ganti simen dalam konkrit bertetulang semakin popular di
kalangan penyelidik dalam menghasilkan konkrit berkekuatan tinggi untuk
kegunaan kejuruteraan struktur. Laporan ini membentangkan keputusan ujikaji
kesan beban statik ke atas rasuk konkrit bertetulang yang dicampur dengan
Metakaolin (MK7003). Peratusan MK7003 yang digunakan dalam campuran konkrit
bertetulang adalah 5%, 10% dan 15% sebagai bahan ganti kepada simen dan 0%
MK7003 dijadikan sampel kawalan. Lapan rasuk bersaiz 1400mm panjang, 150mm
dalam dan 125mm lebar telah diuji, setiap peratusan MK7003 mempunyai dua
sample rasuk. Rasuk dikenakan ujian empat titik beban sehingga gagal. Hasil ujikaji
menunjukkan keupayaan struktur rasuk telah meningkat dengan kehadiran MK 7003.
Pemerhatian juga mendapati MK7003 dengan peratusan gantian sebanyak 10% telah
memberikan keupayaan yang optimum kepada rasuk konkrit bertetulang.
vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
INTRODUCTION
1
1.1 General
2
1.2
Objectives and Scope of Study
3
1.3
Problem Statements
3
1.3.1 High Strength Concrete
3
1.3.2
Cement Replacement Material
3
1.3.3
Structure Behaviour
4
LITERATURE REVIEW
5
2.1
5
Concrete Grade
2.2 High Strength Concrete
2.2.1
2.3
Admixture in High Strength Concrete
7
Metakaolin as Cement Replacement Material of Concrete 9
2.3.1 Introduction of Kaolin
9
2.3.2
Formation of Metakaolin
9
2.3.3
Effects of Metakaolin as a Pozzolan in Concrete 10
2.3.4
Effect of Metakaolin to the Concrete
Compressive Strength
2.4
5
10
Design Condition
12
2.4.1
Concrete Mixes Design
12
2.4.1.1 Workability of Concrete
13
2.4.1.2
The Compressive Strength of Concrete 13
2.4.1.3 Durability of Concrete
2.4.2
15
Design Consideration for Reinforcement
Concrete Beam
17
viii
2.4.2.1
Reinforcement Requirement in Beam
2.5 Structure Behaviour of Reinforced Concrete Beam
2.5.1 Deflection
2.5.1.1
Macaulay’s Method
2.5.1.2
Behaviour of Flexural Member under
Deflection
2.5.2 Cracking
2.5.3
2.6
3
4
17
18
18
19
20
20
2.5.2.1
Cracking under Static Load
21
2.5.2.2
Cracking Mechanism
22
Failure of Beam Subjected to Four Points Load
Modulus Elasticity of Concrete
23
26
METHODOLOGY
30
3.1 Raw Material
30
3.1.1
Preparation of MK7003
30
3.1.2
Ordinary Portland Cement (OPC)
31
3.1.3
Coarse and Fine Aggregate
31
3.1.4
High Yield Deformed and Mild Steel Bars
31
3.1.5 Formwork
33
3.2
Preparation of Beam Specimens
33
3.3
Experimental Set Up
33
3.3.1
Strain Gauge
33
3.3.2
Testing Equipment
33
3.3.3
Static Loading
34
RESULT, ANALYSIS AND DISCUSSION
41
4.1
41
Result
4.1.1
Preliminary Testing
4.1.1.1
4.1.1.2
4.1.2
4.2
41
Concrete Mixed Design and Trial Mix
for Grade 60
41
Reinforcement Tensile Test
42
Static Loading Test Results
42
4.1.2.1
42
Experimental Reading
Analysis and Discussion
42
ix
4.2.1
Ultimate Moment Resistance of the Beam
43
4.2.2
Stress and Strain Relationship
43
4.2.3
Deflection Behaviour
43
4.2.4 Crack Behaviour
5
44
CONCLUSION AND RECOMMENDATION
60
5.1
Conclusion
60
5.2 Recommendation
61
REFERENCES
62
Appendixes A - D
64 - 68
x
LIST OF TABLE
TABLE NO.
TITLE
PAGE
2.1
Chemical composition of OPC and metakaolin.
27
2.2
Relationship between compressive strength and
27
static modulus of concrete.
4.1
Average compressive strength at various
46
MK7003 Contents
4.2
Tensile test result
46
4.3
Data from experimental reading
47
4.4 (a)
Average strain, bending moment and bending stress
for 0%MK7003
4.4 (b)
Average strain, bending moment and bending stress
for 5%MK7003
4.4 (c)
50
Average strain, bending moment and bending stress
for 10% MK7003
4.4 (d)
49
51
Average strain, bending moment and bending stress
for 15% MK7003
52
4.5
Theoretical and experimental load versus deflection
53
4.6
Initial crack load
55
4.7
Theoretical and experimental ultimate moment
4.8
resistance
55
Theoretical and experimental modulus of elasticity
55
xi
LIST OF FIGURES
FIGURES NO
TITLE
PAGE
2.1 (a-c)
Concept of shear and diagonal tension
28
2.2
Flexural shear crack
28
2.3
Shear compression failure
29
2.4
Shear failure
29
3.1
Metakaolin ( MK 7003 )
35
3.2
Beam size and reinforcement detail
35
3.3
Tensile test
36
3.4
Concrete mix
36
3.5
Compaction process
37
3.6
Curing process
37
3.7
Strain gauge location
38
3.8
Diagram of strain gauge location
38
3.9
Test set up
39
3.10
Diagram of test set up
39
3.11
Deflection measurement by tranducer
40
3.12
Measuring of crack by microscope
40
4.1 ( a )
Stress strain relationship 0% MK 7003
56
4.1 ( b )
Stress strain relationship 5% MK 7003
56
4.1 ( c )
Stress strain relationship 10% MK 7003
57
xii
4.1 ( d )
Stress strain relationship 15% MK 7003
4.2
Load versus theoretical and experimental
57
deflections
58
4.3
Initial crack occur at middle span
58
4.4
Location and pattern of crack at failure
59
4.5
Location and pattern of crack for all beams
59
xiii
LIST OF SYMBOLS
As
Cross section area for tension reinforcement
Asc
Cross section area for compression reinforcement
Ac
Cross section area for concrete
b
Width of concrete section
h
Depth of concrete section
z
lever arm distance of concrete section
av
Shear span
I
Moment of inertia
E
Modulus of elasticity
V
Shear force
v
Shear stress
fcu
Concrete compressive strength
fy
Reinforcement tensile strength
xiv
LIST OF APPENDICES
APPENDIX
TITLE
A
Calculation for concrete mix design grade 60
B
Sample calculation for ultimate moment
resistance
C
64
65
Sample calculation for modulus of elasticity
and initial crack theory
D
PAGE
66
Sample calculation for deflection theory by
macaulay method
67
1
CHAPTER 1
INTRODUCTION
1.1
General
The study of High Strength Concrete has become interesting, with the
tendency of concrete building structure to become taller and larger. The importance
has been shown by the Malaysian construction industry for the production of high
strength concrete. An example of the use of HSC is in construction of the Petronas
Twin Towers at the Kuala Kumpur City Centre which high early strength of about
15 N/mm2 were achieved within 12 hours after casting ( Zamin et al, 1995).
The usage of high strength concrete in structure application has been
increasing worldwide and has begun to make an impact in Malaysia. A few years
ago, a characteristic compressive strength of 40N/mm2 would have been considered
high in Malaysia, but now it was become normal phenomena. Nowadays, concrete
with a 28 days curing and has characteristic cube strength of 60N/mm2 and above
will be considered as a high strength concrete. The achievement of such high
strength concrete has been possible primarily through the introduction of materials
such as Metakaolin.
Metakaolin is the most recent mineral to be commercially introduced to the
concrete construction industry. A few report investigated the potential of local
kaolin from several areas in Malaysia such Tapah, Perak and Johor. Metakaolin the
product of processed heat treatment of natural kaolin is widely reported as a quality
2
and effective pozzolanic material, particularly for the early strength development. In
addition to pozzolanic reaction, the action of micro filler has been reported to partly
improve strength development of cement-metakaolin mortar (Sabir et al, 2001).
There are several advantages of incorporating metakaolin to produce high
strength for high rise building. These include reductions in member thickness
resulting in reduced foundation loads, increased rentable areas and smaller structural
element, as well as high early strength development of concrete which allows early
stripping of formwork, thus speeding up concrete construction.
The HSC fracture behaviour is being studied with great seriousness. High
strength concrete is nearer to linear theories of fracture and is relatively more brittle.
The challenge is whether one can make high strength concrete relatively more
ductile by improving the cohesiveness of cracks.
1.2
Objectives and Scope of Study
The objective of this study is to determine the structural behaviour of high
strength concrete beam grade 60 N/mm2 with replacement of 5%, 10% and 15%
MK7003 to weight of ordinary Portland cement due to static load. The water binder
ratio is fixed at 0.35 and cured in room temperature. Parameters to be investigated
include cracking, deflection, moment resistance and modulus of elasticity due to
bending.
Laboratory experiment will be conducted in the Civil Engineering Laboratory,
UiTM Pulau Pinang, using 1000 kN Universal Testing Machine. The result will
identify the following responses:
i) Mid span deflection
ii) Initial crack occur
3
iii) Location of crack and type of crack failure
iv) Moment resistance of the beam
v) Modulus of elasticity due to bending.
1.3
Problem Statement
This chapter will discuss the justification and the requirement of the study.
The three main aspects such as high strength concrete, cement replacement material
ie. MK 7003 and structure behaviour will be explain detail to support the
justification in this study.
1.3.1
High Strength Concrete
The tendency of concrete building structures to become taller and simpler
has led to the:
i)
Increased the member size dimension and heavily loaded columns in high
rise building structure.
ii)
The need to design flat slabs economically, constrain of the punching effect
would lead to undesirably thick slabs.
The necessity of using higher strength concrete to obtain columns of reduced
section and floor systems without internal beams, for heavy loaded structure is
obvious sometimes without any beam. In the case of columns, the increase of
concrete strength often result in more economical sections, while allowing increased
usable floor space.
4
For flat slabs, the main reason to use higher strength is to obtain minimum slab
height with sufficient punching shear resistance.
1.3.2
Cement Replacement Material (CRM)
The construction industry has taken considerable strides forward over the last
two or three decades with regard to many materials, in particular – High Strength
Concrete and generally High Performance Concrete.
The development of new technology in the material sciences is progressing
rapidly. Advanced composite construction material and HSC/HPC are gaining wide
acceptance in the construction industry of today, and are well positioned for
increasing proliferation in use in the future. HSC and HPC will continue to make
important contributions to the enhanced quality and efficiency in the construction of
infrastructure and our communities in the next century.
The utilization of high strength and high performance concrete has been
increasing throughout the world. Amongst the various methods used to improved the
strength and performance of concrete, the use of CRM like MK7003 is a relatively
new approach.
1.3.3
Structure Behaviour
Visual behaviour is very important in assessing the reason for deterioration
of concrete structures. The first stage in an evaluation of concrete structure is to
study the condition of the concrete, to note any defect in the concrete. Among of the
important are the presence of cracking, the crack propagation and deflection of the
5
structure. Visual assessment determine whether or not to proceed with detailed
investigation.
The understanding of fracture mechanism of RC structure is important and
under this study its focusing to crack and deflection behaviour for RC beam under
static loading.
6
CHAPTER 2
LITERATURE REVIEW
2.1
Concrete Grade
The grade of concrete is defined as that number, which indicated the
characteristic compressive strength of concrete in N/mm2, determined by cubes test
made at 28 days. Thus grade 60 concrete has a characteristic strength of 60 N/mm2.
This grade 60 of concrete is used to produce high strength of concrete.
2.2
High Strength Concrete
In the early 1970s, experts predicted that the practical limit of ready mixed
concrete would be unlikely to exceed a compressive strength greater than 11,000 psi
(43 MPa). Over the past two decades, the development of high-strength concrete has
enabled builders to easily meet and surpass this estimate. Two buildings in Seattle,
Washington, contain concrete with a compressive strength of 19,000 psi (131 MPa).
The primary difference between high-strength concrete and normal-strength
concrete relates to the compressive strength that refers to the maximum resistance of
a concrete sample to applied pressure. Although there is no precise point of
separation between high-strength concrete and normal-strength concrete, the
American Concrete Institute defines high-strength concrete as concrete with a
compressive strength greater than 6000 psi (41 MPa).
7
Manufacture of high-strength concrete involves making optimal use of the
basic ingredients that constitute normal-strength concrete. Producers of highstrength concrete know what factors affect compressive strength and know how to
manipulate those factors to achieve the required strength. In addition to selecting a
high-quality portland cement, producers optimize aggregates, then optimize the
combination of materials by varying the proportions of cement, water, aggregates,
and admixtures.
When selecting aggregates for high-strength concrete, producers consider the
strength of the aggregate, the optimum size of the aggregate, the bond between the
cement paste and the aggregate, and the surface characteristics of the aggregate. Any
of these properties could limit the ultimate strength of high-strength concrete.
High strength concrete (HSC) is not fundamentally different from normal
strength concrete. It is different in its level and strength and associated properties
and their ramifications. It is interesting to consider, as a very elementary approach to
the nominal compressive strength, the three elements of concrete namely paste,
aggregate and paste-aggregate bond. In high strength concrete, the paste is hard,
strong aggregate are used with crushing strength of perhaps 200 N/mm2 and higher.
Therefore failure in the concrete seems likely to be initiated at the aggregate or paste
interface. In the other words, the strength of concrete is depending on the bond
strength of paste aggregates. In this study, the high HSC refers to the concrete
obtained through using Ordinary Portland Cements cured at normal temperatures.
The total cementitious material will be typically around 415 to 650 kg/m3.
Generally, HSC is to be extremely useful in the construction of high rise
building and other large structures in that with their use the structural element of
these structures become reasonable such as bridges, coastal and offshore structures,
prestressed structural components, airport and road pavement and compressive
structures.
Optimum concrete mixture design result from selecting locally available
materials that make the fresh concrete placeable and finishable and that ensure the
strength development and other desired properties of hardened concretes is achieved.
8
Some of the basic concept that needs to be understood for higher strength concrete
is:
i)
Aggregate should be strong and durable. They need not necessarily be
hard and of high strength but need to be compatible, in term of stiffness
and strength, with the cement paste. Generally smaller maximum size
coarse aggregate is used for higher strength concretes.
ii)
High strength concrete mixtures will have a high cementitious material
contents.
iii)
HSC mixtures generally need to have low water cementitious material
ratio. This low water cementitious ratio may need water reducing
admixtures ie superplasticizer.
iv)
The total cementitious materials content will be around 415 kg/mm3 to
650kg/ mm3.
2.2.1
Admixtures in high strength concrete.
Concrete is probably the most extensively used construction material in the
world. It is only second to water as the most heavily consumed substance with about
six million tones being produced every year. This is largely due to the abundance of
raw materials for cement manufacture, low relative cost and the versatility and
adaptability of concrete in forming various structural shapes. However,
environmental concern both in term of damage caused by the extraction of raw
material and CO2 emission during cement manufacture have brough about pressures
to reduce cement consumption by the use of supplementary materials. These
materials may be naturally occurring, industrial wastes or by products or those that
require relatively less energy to manufacture. Other concerns that have contributed
9
to these pressures are related to the increase in the number of incidents where
concrete structures have experienced serious deterioration.
In addressing these concerns and other environmental problems relating to
the disposal of waste industrial by products and also because of economic
advantages, mixture of Portland cement and pozzilana are now very commonly used
in concrete production.
Originally the term pozzolan was associated with naturally formed volcanic
ashes and calcined earths, which react with lime at ambient temperatures in the
presence of water.
Pozzolans, such as fly ash and silica fume, are the most commonly used
mineral admixtures in high-strength concrete. These materials impart additional
strength to the concrete by reacting with portland cement hydration products to
create additional C-S-H gel, the part of the paste responsible for concrete strength.
It would be difficult to produce high-strength concrete mixtures without
using chemical admixtures. A common practice is to use a superplasticizer in
combination with a water-reducing retarder. The superplasticizer gives the concrete
adequate workability at low water-cement ratios, leading to concrete with greater
strength. The water-reducing retarder slows the hydration of the cement and allows
workers more time to place the concrete.
High-strength concrete is specified where reduced weight is important or
where architectural considerations call for small support elements. By carrying loads
more efficiently than normal-strength concrete, high-strength concrete also reduces
the total amount of material placed and lowers the overall cost of the structure.
The most common use of high-strength concrete is for construction of highrise buildings. At 969 ft (295 m), Chicago's 311 South Wacker Drive uses concrete
with compressive strengths up to 12,000 psi (41 MPa) and is the tallest concrete
building in the United States.
10
2.3
Metakaolin as Cement Replacement Material Concrete.
2.3.1
Introduction of Kaolin.
The raw material input in the manufacture of metakaolin (MK) is kaolin clay.
Kaolin is a fine, white, clay mineral that has been traditionally used in the
manufacture of porcelain. It is thought that the term kaolin is derived from the
Chinese Kaoling, which translates loosely to white hill and has been related to the
name of a mountain in China that yielded the first kaolins that were sent to Europe.
Kaolinite is the mineralogical term that is applicable to kaolin clays.
Kaolinite is defined as a common mineral, hydrated aluminum disilicate,
Al2Si2O5(OH)4, the most common constituent of kaolin (Megat J. 2001).
2.3.2
Formation of Metakaolin
The meta prefix in the term is used to denote change. It is a borrowing from
Greek meaning after, along with, beyond. It is used, and is recognizable, in the
formation of compound words: metabolic, metamorphosis. The scientific use of the
prefix is used for a combining form denoting the least hydrated of a series.
In the case of metakaolin, the change that is taking place is
dehydroxylization, brought on by the application of heat over a defined period of
time. At about 100-200 degrees C, clay minerals lose most of their adsorbed water.
The temperature at which kaolinite loses water by dehydroxilization is in the range
of 500-800 degrees C. This thermal activation of a mineral is also referred to as
calcining.
Beyond the temperature of dehydroxylization, kaolinite retains two-
dimensional order in the crystal structure and the product is termed metakaolin.
11
The key in producing metakaolin for use as a supplementary cementing
material, or pozzolan is to achieve as near to complete dehydroxilization as possible
without over heating. Successful processing results in a disordered, amorphous
state, which is highly pozzolanic. Thermal exposure beyond a defined point will
result in sintering and the formation of mullite, which is dead burnt and not reactive.
In other words, kaolinite, to be optimally altered to a metakaolin state, requires that
it is thoroughly roasted but never burnt (Sabir et al, 2001).
The term MK7003 is referred to the Malaysian kaolin which from finding
shown the optimum calcining temperature is at 7000 C in three hours.
2.3.3
Effects of metakaolin as a Pozzolan in Concrete
Pozzolan can define a siliceous or aluminous material which in itself
possesses little or no cementitious value but will, in finely divided form and in the
presence of moisture, chemically react with calcium hydroxide at ordinary
temperatures to form compounds possessing cementitious properties (Neville
A.M.1987).
Pozzolanic reaction in concrete;
C3 S / C2 S ( Clinker ) + H2 O -Æ Calcium Silicate Hydrates (CSH) + Ca (OH)2
Ca(OH)2 + MK Æ CHS + Crystalline product.
Once the MK used in the concrete, it will react with calcium hydroxide to
form calcium silics hydrated. Formation of hydrated calcium silica in pozzolanic
activity will allow the MK to be used as partial cement replacement material. The
chemical compositions of the OPC and the MK are given in Table 2.1.
12
2.3.4
Effect of MK to the concrete compressive strength
MK, the product of processed heat treatment of natural kaolin, is widely
reported as a quality and effective pozzolanic material, particularly for the early
strength development. A few reports investigated the pozzolanic potential of local
kaolin from several areas in Thailand, mainly used in ceramic industry, for the use in
concrete industry. The effective range of burning temperature and grinding process
for local kaolin of 750-800 o C and 6 hours have been reported (Jirawat et all 2002).
In addition to pozzolanic reaction, the action of micro filler has been reported
to partly improve strength development of cement–metakaolin mortar.
For concrete, the strength improvement especially during the first 3 days was
observed. The increases in compressive and flexural strength were in the range of
13-18% and 1-16% respectively. An optimum percentage replacement of 20% was
found for strength improvement. Significant microstructure improvement was
revealed through the very high level of chloride ingress resistance, compared to the
medium level of high strength concrete. The potential as a low cost, locally
produced, supplement material for repair material and high strength and durable
concrete was high (Jirawat et al, 2002).
On the basis of investigation carried out to study the effect of metakaolin, it
has been found that the metakaolin used in different dosages to replace the Portland
cement changes properties of both the fresh and hardened concretes. It increases the
compressive strength and reduces the slump for a given aggregate-binder ratio and
water-binder ratio. The effect of using metakaolin as a cement replacement material
on air permeability was found to be very marginal. Up to a maximum of 10%
replacement level, the sorptivity of concrete is improved for high levels of cement
content. However, there is relatively little improvement in sorptivity at low levels of
cement content.
There have been several studies on the strength development of concrete
containing MK. These studies have demonstrated clearly that with intelligent use
13
considerable enhancement in strength, particularly at the early stages of curing, can
be produced. Caldarone et al. produced concrete with 5% and 10% MK, which
showed enhanced strengths at ages up to 365days. They reported that their MK-PC
concrete exhibited strengths, which were slightly greater than silica fume Portland
cement mixture at the same levels of cement replacement by the pozzolans.
Similar influences of MK on the strength of concrete have been reported by
Wild et al. The authors identify three elementary factors, which influence the
contribution that MK makes to concrete strength. These are the filler effect, which is
immediate, the acceleration of PC hydration, which occur within the first 24 hours,
and the pozzolanic reaction, which has its maximum effect within the first 7 – 14
days for all MK level between 5% and 30%. The degree to which strength is
enhanced decline beyond 14 days, although strength gains relative to the control are
still present after 90 days.
The influence of curing temperature on the strength development in concrete
containing up to 15% MK was studied by Sabir. It was shown that curing MK
concrete at 50 C results in increased early strength compared to the strength of
specimens cured at 20C. The acceleration in strength development due to the high
curing temperature diminishes in the long term (365 days). In term of the strength
relative to that of the control concrete cured at 20 C, the optimum level of MK
replacement for cement in concrete with water binder ratio 0.35 cured at 20 C was
found to be about 10%. This level of MK was found to be reduced to about 5% for
concrete cured at higher temperature (50 C) and with higher water binder ratio 0.45.
2.4
Design Condition
2.4.1
Concrete Mixes Design
This part is normally describes in terms of proportions by weight of materials
which they contain or in terms of the strength required of the concrete at a particular
14
age. Mixed design is the choosing of the ingredients to provide economical, concrete
desired properties. It implies the deliberate proportioning of the cement, fine and
course aggregate and water, taking into account, of only the specified concrete
particles but also the characteristic of the materials used.
There are various factor involved in the process of designing a concrete mix.
In order to clarify the sequence of operation, and for ease of reference, the flow
process is devided into five stages. Each of these stages deals with a particular
aspect of the design and ends with an important parameter or final unit proportion.
The stages of mix design process as shown below:
Stage 1 : Deals with strength leading to the free water cement ratio
Stage 2 : Deals with workability leading to the free water content
Stage 3 : Combine result of stage 1 and 2 to give the cement content
Stage 4 : Deals with the determination of the total aggregate content
Stage 5 : Deals with the selection of the fine and aggregate content
The problem of designing a concrete mix consist of selecting the correct
proportions of cement, fine and course aggregate and water, to produce concrete
which having the specified properties. The most properties usually specified are:
i)
The workability of the fresh concrete
ii)
The compressive strength of concrete
iii)
The durability of concrete
2.4.1.1 Workability of Concrete
For practical purpose, workability implies the ease with which a concrete
mix can be handled from the mixer to its finally compacted shape. The three main
characteristics of workability portray consistency, mobility and compatibility.
Optimal workability would give maximum density, minimum void and no
segregation.
15
Factors Effecting Workability
The workability of concrete is affected by several numbers of factors such as water
content, time and temperature, type of cement, aggregates etc.
i)
Water Content
The main factor is the water content of the mix, expressed in kilogram (or
litres) of water per cubic metre of concrete. It is convenient, though approximate,
to assume that, for a given type of grading and workability of concrete, the water
content is independent of the aggregate /cement ratio or of the cement content of the
mix. If the water content and the other mix proportions are fixed, workability is
governed by maximum size of aggregate, its grading, shape and texture. Aggregate
particles, which have sharp edges and a rough surface, such as crushed stone, need
more water than smooth and rounded particles to produce concrete of the same
workability.
As a general rule it can be said that at the same water/cement ratio, a crushed
aggregate concrete may have a higher strength than a smooth or rounded aggregate
concrete. The fine and course aggregates should be proportioned to obtain the
required degree of workability with minimum amount of water.
ii)
Type Of Cement
Different types of cement have different water requirements to produce
pastes of standard consistence. Different types of cement also will produce concrete
have a different rates of strength development. The choice of brand and type of
cement is the most important to produce a good quality of concrete. The type of
cement affects the rate of hydration, so that the strengths at early ages can be
considerably influence by the particular cement used. An average. Ordinary Portland
Cement will give a concrete with about 80% to 85% of the strength obtained with an
average of Rapid Hardening Portland Cement, of the same mix proportions, at 7
days. For the 28 days it may about 90% of the strength of rapid hardening cement.
16
iii)
Aggregates
Aggregates generally occupy about 70 to 80% of the volume of concrete and
there fore can be expected to have an important influence on its properties. Clearly it
is important that the chosen aggregate should contain no constituent who might
adversely affect the hardening of the cement or the durability of the hardened mass
aggregate shape and texture affect the workability of fresh concrete through their
influence on cement paste requirement. Sufficient paste is required to coat the
aggregates and to provide lubricating to decrease interactions between aggregate
particles during mixing. In order to be able to promotion suitable concrete mixes,
certain properties must be known such as shape and texture, size gradation, moisture
content, specific gravity and bulk unit weight. These properties influence the paste
requirements for workable fresh concrete (Neville A. M. 1987).
2.4.1.2 The Compressive Strength of Concrete
With given proportions of aggregates the compressive strength of concrete
depends primarily upon age, cement content and the water /cement ratio, an increase
in any of these factors producing an increase in strength.
Mixing of Fresh Concrete
The objective of mixing is to coat the surface of all aggregate particles with
cement paste and blend the ingredients into a uniform mass. The method of mixing
can either in rotation or stirring operation. The rotation operation is used in tilting
drum mixer, tilting drum mixer, non tilting drum mixture, dual drum mixer and
continues mixer. While the stirring operation was used in a pan type mixer.
Age at Test and Curing Conditions
The strength developed by concrete made with given materials and given
proportions increases for many months under favorable conditions, but in the
17
majority of specifications the strength is specified at an age of 28 days. The strength
development of concrete made with all types of Portland cement depends on the
temperature and humidity conditions during curing. Higher temperatures increase
the speed of the chemical reaction and thus the rate of strength development, and in
order to achieve higher strengths at later ages loss of water from the concrete must
be prevented. For test purposes the concrete test specimens is stored in water at a
constant temperature as specified in BS 1881: Part 3.
2.4.1.3 Durability of Concrete
Durability of concrete can be defined as the ability of concrete to withstand
the damaging effects of the environment and of its services conditions without
deterioration for along period of time.
Therefore it is essential that concrete is designed in such a way that it may be
of service without deterioration over a period of years. Such concrete is said to be
durable. The absence of durability may be caused either by the environment to
which the concrete is exposed or by internal cause within the concrete itself. The
external causes can be physical, chemical or mechanical: they may be due to
weathering, occurrence of extreme temperature, abrasion, electrolytic action and
attack by natural or industrial liquids and gases. The extent of damage produced by
these agents depends largely on the quality of the concrete, although under extreme
condition any unprotected concrete will deteriorate.
The internal causes are the alkali aggregate reaction, volume change due to
the difference. The durability of concrete is one of the important properties because
it is essential that concrete should be capable of withstanding the conditions for
which it has been designed throughout the life of a structure. Lack of durability can
be caused by external agents arising from the environment or by internal agents
within the concrete. The external causes include the effects of environment and
service conditions to which concrete is subjected such as weathering, chemical etc.
18
The internal causes are effects of salt, particularly chlorides and sulfates (Neville
A.M 1987).
Specifications, based on British Standard, usually contain clauses which deal
with durability requirements for concrete subjected to different, defined, condition
of exposure and they provide the constraints on the mix design.
The concrete is exposed or by internal cause within the concrete itself. The
external causes can be physical, chemical or mechanical: they may be due to
weathering, occurrence of extreme temperature, abrasion, electrolytic action and
attack by natural or industrial liquids and gases. The extent of damage produced by
these agents depends largely on the quality of the concrete, although under extreme
condition any unprotected concrete will deteriorate.
The internal causes are the alkali aggregate reaction, volume change due to
the difference. The durability of concrete is one of the important properties because
it is essential that concrete should be capable of withstanding the conditions for
which it has been designed throughout the life of a structure. Lack of durability can
be caused by external agents arising from the environment or by internal agents
within the concrete. The external causes include the effects of environment and
service conditions to which concrete is subjected such as weathering, chemical etc.
The internal causes are effects of salt, particularly chlorides and sulfates (Neville
A.M 1987)
Specifications, based on British Standard, usually contain clauses which deal
with durability requirements for concrete subjected to different, defined, condition
of exposure and they provide the constraints on the mix design.
19
2.4.2 Design Consideration for Reinforcement Concrete Beam.
Generally, reinforced concrete beam design consists primarily of producing
member detail, which will adequately resist the ultimate bending moments, shear
forces and torsional moments. At the same time, serviceability requirements must be
considered to ensure that the member will behave satisfactorily under working loads.
It is difficult to separate these two criteria, hence the design procedure consists of
the series of interrelated steps and checks. These are three basic stages, which are
important in designs, these stages must be followed in order to get the accurate
results.
The three stages are:
•
Preliminary analysis and member sizing
•
Detailed analysis and design of reinforcement
•
Serviceability conditions
2.4.2.1 Reinforcement Requirement in Beam.
Minimum area of reinforcement
For most purpose, thermal and shrinkage cracking may be controlled within
acceptable limits by use of minimum reinforcement quantities specified by BS 8110.
- For tension reinforcement of rectangular section ;
100As/Ac = 0.13%
- For compression reinforcement of rectangular beam;
(2.1)
20
100Asc/Ac = 0.2%
(2.2)
Maximum area of reinforcement
These are determined largely from the practical need to achieve adequate
compaction of the concrete around reinforcement. The limit specified by BS 8110
are as follow.
100As/bh or
100Asc/bh < 4 %
(2.3)
For this experiment the design is followed the previous experiment detailed
of beam (Amer 1999), since the reinforcements detail are in range of maximum and
minimum reinforcement were calculated.
2.5
Structure Behaviour of Reinforced Concrete Beam
2.5.1
Deflection
There are important relation between applied load and stress (flexural and
shear) and the amount of deformation or deflection that a beam can exhibit. In
design of beam, it is important to limit the deflection for specific load. So, in these
situation, it is not enough only to design for the strength (flexural normal and
shearing stresses), but also for excessive deflection of beams. Failure to control
beam deflection is frequently reflected by the development of crack in plastered
walls and ceiling.
The commonly method used to determine beam deflection is double
integration method. This method involving the process of established the differential
equation that governs beam deflection. The basis of this differential equation is that
21
plane sections within the beam remain plane before and after loading and the
deformation of the fibre ( elongation and contraction ) is proportional to the distance
from natural axis.
Assumption been made on elastic curve equation are;
i)
The beam deflection due to shearing stress is negligible
ii)
The value of elastic modulus, E and second moment of inertia, I
remain constant along the beam.
This equation is useful only when the bending moment with function of certain
length of span is constant for the interval of the beam involved. For most beams,
however this moment is not constant and certain mathematical modification is need
to make it applicable for the whole span like Macaulay’s method.
2.5.1.1 Macaulay’s Method
This theoretical method is based on double integrated method which consists
of derivation of elastic curved of beam and further the development of differential
equation of the elastic curve for a beam is established.
EI (d2y/dx2) = M (x)
Where;
E
= Modulus of elasticity for the material;
I
= Moment of inertia about neutral axis;
M (x) = Bending Moment along the beam as function x.
From the equation, the deflection of a beam depends on four general factors;
i)
Stiffness of the material that the beam is made of;
ii) Length of beam;
(2.4)
22
iii) Applied loads; and
iv) Types of beam supports.
2.5.1.2 Behaviour of flexural Member under Deflection
When a flexural member subjected to a bending moment, the distinctly
different stress configuration member at a various cross sections will apply along the
span. In addition, a tension and compression zone will occur which is divided by
neutral axis. When a greater moment applies to the flexural member, the concrete
fails at the outer fibers of the tension and minute cracks are formed at random
intervals.
At places of still greater moment the tensile failure in the concrete is more
extensive, cracking extends closer to neutral axis and cracks widen. However the
concrete between cracks still carries some tension. Owing to this fact, the tensile
stress in the steel between the cracks is less than that at the cracks (Chong et
al.1994).
They are two phases in the short-term response of a typical beam. When the
applied loads are small and section has not cracked. In this stage, the uncracked
section behaviour predominates. It is greater applied load in which the cracked
section dominates.
2.5.2
Cracking
In general, tensile cracking will occur in an economically design reinforced
concrete member even under service load. Tensile cracking develops when concrete
with a limited capacity for elongation tends to deform with the tensile reinforcement
23
through the bonding action. Mechanism of cracking is based on redistribution of
concrete stress at crack formation that is compatible with observed internal and
surface cracking.
In reinforced concrete structures, one of the requirements for the
serviceability limit state is that cracking of concrete shall not adversely affect the
appearance or durability of the structures. The spacing and width cracks in
nominally identical structures varies between wide limits, so sufficient testing was
done to provide a sound statistical basis for the design method.
The recommended limits are those which have a 20 % probabilities of being
exceed when full design load for serviceability limit state acts on the structure. In
designing reinforced concrete structures, it is rarely necessary to calculate crack
width, for it has been found that satisfactory crack control can be obtained if the
spacing of reinforcing bars does not exceed certain limits, calculated from the crackwidth equations (Johnson, 1975).
Subcritical crack growth is a commonly observed but still not well
understood phenomenon. It is generally identified with the process of slow crack
growth in metals subjected to rising or cyclic load. The phenomenon, however, it is
exclusively associated neither with ductile fracture nor with plastic deformation.
Cracks can spread slowly in an elastic stress environment as long as the crack
driving force is kept below critical state. More precisely, it is the combined
interaction of loading geometry and size specimen, material; and environment that
determines the crack growth characteristics (Sih G. C.,1983).
2.5.2.1 Cracking Under Static Load
A classical mechanism for cracking of reinforced concrete members, that has
been proposed in most of the studies of the surface cracking phenomenon, is based
on assumptions that tensile stresses in concrete are uniform, distributed over on
24
effective cross section and that a certain distribution of bond stresses exist along the
reinforcement.
Normally micro cracking occurs in concrete even before external loads are
applied. These initial cracks are due to non-uniform volume changes resulting from
shrinkage of cement paste, built up of corrosion products around reinforcement or
expansion of aggregates. Crack initiate at critical locations where the limiting tensile
properties of the concrete have been exceeded due to weak material or high stress
and strain. Initial cracks, which are randomly located through the concrete,
propagate to the surface of a reinforced concrete member under relatively lower
external loads.
Additional crack develops in reinforced concrete between primary cracks
under higher external loads. These cracks are due to the difference of extendibility
between concrete and reinforcement and to the bonding between the two.
The surface cracking phenomenon of reinforced concrete element that is
gradually subjected to tension occurs in three stages, which are:
i)
First stage of cracking is concerned with primary cracks that form at
random critical section.
ii)
Second stage of cracking is concerned with the formation of secondary
cracks between random primary cracks.
iii)
Third stages of cracking, also referred to as equilibrium stage, occurs
when no additional surface cracks form during further increases in the
applied load.
2.5.2.2 Cracking Mechanism
A classical mechanism for cracking of reinforced concrete members, that has
been proposed in most of the studies of the surface cracking phenomenon, is based
on assumptions that tensile stresses in concrete are uniform, distributed over an
25
effective cross section and that a certain distribution of bond stresses exist along
reinforcement.
Crack formation is assumed to occur as the external load gradually as follows:
i)
Primary cracks were formed at random critical sections, where the
uniform tensile strength occurs. A slip occurs between the concrete of
reinforcing bar at the primary section. Concrete surfaces at the crack
section are free of stresses and the force in the reinforcement equals to
the external load.
ii)
Concrete tensile stresses are present between the primary cracks, this is
because of bonding action, that takes place as the concrete, tend to
deformed with the forcing steel. Distribution and magnitude of the bond
stress between the concrete and reinforcement will determine the
distribution of the concrete stress between the primary crack sections.
iii)
When external load increases and the uniform concrete stress exceeds the
tensile strength, the formation of new crack will occur. The cracking will
propagate until the stress does not exceed the concrete strength.
2.5.3
Failure of beam subjected to four points loading.
Figure 2.1 (a) shows half of a reinforced concrete beam acted on by a shear
force V. An element in the beam would be subjected to shear stresses v, as in Figure
2.1 (b) and to horizontal normal stresses due to bending. If the element is near the
neutral axis or within a flexurally cracked region, the bending stresses are
comparatively small and may be neglected without serious loss in accuracy. The
shear stresses in Figure 2.1 (b), in which the principal tensile stresses are
traditionally called the diagonal tension stresses. It can be seen that when the
26
diagonal tension stresses reach the tensile strength of the concrete, a diagonal crack
will develop.
The preceding description, through convenient as an introduction to the
concepts of diagonal tension and diagonal cracking, does not give a whole picture of
the actual behaviour. In, fact the type of diagonal crack in Figure 2.1 (c) called web
shear crack, occurs mainly in prestressed beams and only rarely in reinforced
concrete beam. Of course, the behaviour of reinforced concrete beam is much
influenced by the shear stresses, but the trouble is that we do not know how to
calculate their values. In the earlier days it was usual to make various assumptions
(which were not justified) and to prove that, below the neutral
axis, v was
everywhere equal to V/bz (b being the beam width and z the lever arm distance) and
that, above the neutral axis, v varied parabolically to zero at the compression face of
the beam. It was realized that things were not so simple. Even today, the distribution
of the shear stress across a flexurally cracked beam is not understood and an
accurate determination of the magnitude of v is impossible; indeed present day
designer no longer attempt to calculate the actual value of the shear stress v.
However, there are advantages in retaining the concept of a nominal shear stress to
be used as some sort of stress coefficient in design. In current British design
practice, BS 8110 refers to this nominal shear as the design shear stress. For a
rectangular beam, the failure mode is strongly dependent on the shear span / depth
ratio, av / d;
i)
av / d > 6 : Beams with such a high av / d ratio usually fail in bending;
ii)
2.5 < av / d < 6 : Beams with av / d lower than about 6 tend to fail in
shear. With reference to Figure 2.1 (a), as the force V is increased, the
flexure crack a-b, nearest the support would propagate towards the
loading point, gradually becoming an inclined crack, which is known as a
flexural shear crack but which is often referred to simply as a diagonal
crack (Figure 2.2: crack a-b-c). With further increase in V, failure usually
occurs in one of two modes. If the av / d ratio is relatively high, the
diagonal crack would rapidly spread to e, resulting in collapse by
splitting the beam into two pieces. This mode of failure is often called
27
diagonal tension failure; for such a failure mode, the ultimate load is
sensibly the same as that at the formation of the diagonal crack. If the
av/d ratio is relatively low, the diagonal crack tends to stop somewhere at
j (Figure 2.2); a number of random cracks may develop in the concrete
around the longitudinal tension reinforcement. As V is further increased,
the diagonal crack widens and propagates along the level of the tension
reinforcement (Figure 2.2 : crack g-h). The increased shear force presses
down the longitudinal steel and causes the destruction of the bond
between the concrete and the steel, usually leading to the splitting of the
concrete along g – h. If the longitudinal reinforcement is not hooked at
the end, the destruction of bond and the concrete splitting will cause
immediate collapse. If hooks are provided, the beam behaves like a twohinge arch until the increasing force in the longitudinal reinforcement
destroys the concrete surrounding the hooks, hence collapse occurs. This
failure mode is often called shear tension failure or shear bond failure;
again the ultimate load is not much higher than the diagonal cracking
load.
iii)
1 < av / d < 2.5 : For av / d lower than about 2.5 but greater than 1, the
diagonal crack often forms independently and not as a development of a
flexural crack (Figure 2.3). The beam usually remains stable after such
cracking. Further increase in the force V will cause the diagonal crack to
penetrate into the concrete compression zone at the loading point, until
eventually crushing failure of the concrete occurs there, sometimes
explosively (Figure 2.3: shaded portion). This failure mode is usually
called shear compression failure; for this mode, the ultimate load is
sometimes more than twice that at diagonal cracking.
iv)
av / d < 1 : The behaviour of beams with such low av / d ratio approaches
that of deep beams. The diagonal crack forms approximately along a line
joining the loading and support points (Figure 2.4). It forms mainly as a
result of the splitting action of the compression force that is transmitted
directly from the loading point to the support; it initiates frequently at
about d/3 above the bottom face of the beam. As the force V is increased,
28
the diagonal crack would propagate simultaneously towards the loading
and support points. When the crack has penetrated sufficiently deeply
into the concrete zone at the loading point, or, more frequently, at the
support point, crushing failure of the concrete occurs. For a deep beam
failure mode, the ultimate load is often several times that at diagonal
cracking.
2.6
Modulus Elasticity of Concrete
The modulus of elasticity is generally related to the compressive strength of
concrete. This relationship depends on the aggregate type, the mix proportions,
curing condition, rate of loading and method of measurement (Ahmad et al 1994).
Table 2.2 has shown the relationship between strength and modulus of elasticity as
stated in BS 8110:Part 2: Clause 7.2.
29
Table 2.1 : Chemical Composition of OPC and Metakaolin (MK)
Chemical Composition
OPC ( %)
MK ( %)
SiO3
20.69
51.6
Al2O3
4.72
41.3
Fe2O3
CaO
MgO
3.06
63.76
2.08
4.64
0.09
0.16
TiO2
0
0.83
SO3
2.92
0
K2O
0.61
0.62
Na2O
LOI
0.26
0.87
0.01
0
Table 2.2 : Relationship between compressive strength, fcu and static modulus
of concrete, E
Compressive Strength, fcu
(N/mm2)
Static Modulus, E
Mean Value
Typical Range
(kN/mm2)
(kN/mm2)
20
24
18 to 30
25
25
19 to 31
30
26
20 to 32
40
28
22 to 34
50
30
24 to 36
60
32
26 to 38
30
Figure 2.1 (a – c) : Concept of shear and diagonal tension
Figure 2.2 : Flexure-shear crack
31
Figure 2.3 : Shear-compression failure
Figure 2.4 : Shear failure
32
CHAPTER 3
METHODOLOGY
In this chapter, the material used and the preparation of the specimens were
described. Details of the test set up and the procedure of testing are explained.
3.1
Raw Materials
Raw materials listed below were used for preparation of the specimens:
i)
Ordinary Portland Cement (OPC)
ii)
Crushed Coarse Aggregate with 20mm maximum size
iii)
Uncrushed Sand with 5 mm maximum size
iv)
Steel Reinforcement:
-
High Yield for main bar (460MPa) and;
-
Mild steel for shear reinforcement (250MPa)
v)
Kaolin to produced Metakaolin (MK7003)
vi)
Plywood with thickness 12 mm and timber to prepared formwork.
33
In this experiment, eight numbers of R.C. beam with the variation percentage
replacement of MK7003 by weight to ordinary Portland cement were cast. Size
beam are 125mm in width by 150mm in depth and 1400mm length.
3.1.1
Preparation of MK7003
MK7003 has prepared by calcinations of kaolin process at 7000 C in ash
furnace for three hours, Figure 3.1 was shown the MK7003. The raw kaolin was
supplied by Associated Kaolin Industries Bhd (AKI) Tapah Perak. For the purpose
of this study, the variation amounts of MK7003 are used.
3.1.2
Ordinary Portland Cement (OPC)
OPC are supplied by local supplier and all mixes contain total cement
content of 543 kg/m3 where MK7003 as a cement replacement material in the mixes.
3.1.3
Coarse and Fine Aggregate
The course aggregate from granite materials with particle size of between
10mm to 20mm. The fine aggregate from river sand with maximum size of 5mm.
34
3.1.4
High Yield Deformed and Mild Steel Bars
For each specimen, two numbers of high yield bars of 16mm diameter are
used as tension bars and two numbers of 6mm mild steel bars as compression bars.
The minimum area of tension reinforcement of rectangular section (for fy = 460
N/mm2), using equation 2.1;
100As / Ac = 0.13
As
= 0.13 (125 x 150) / 100
= 25 mm2
The minimum area of compression reinforcement of rectangular section (for fy = 460
N/mm2), using equation 2.2;
100Asc / Ac = 0.2
Asc
= 0.2 (125 x 150) / 100
= 37.5 mm2
The maximum area of tension and compression reinforcement, using equation 2.3;
100As /bh or 100Asc / bh < 4 %
As or Asc
= 4 (125 x 150) / 100
= 750 mm2
Area for applied compression bar, Asc app. = π( r )2 x 2nos;
π( 3 )2 x 2nos =
57 mm2
Asc min = 37.5 mm2 < Asc app = 57 mm2 < Asc max =750 mm2 Æ ok satisfied.
Area for applied tension bar, As app. = π( r )2 x 2nos;
π( 8 )2 x 2nos =
402 mm2
35
As min = 25 mm2 < As app = 402 mm2 < As max =750 mm2
Æ ok satisfied.
Both top and bottom bar are satisfied the minimum and maximum
requirement of beam as stated in BS 8110 with size of 125mm width and 150mm
depth. The beam and reinforcement detail are shown in Figure 3.2.
In order to control shear stresses in the concrete beam, mild steel stirrups
with size 6mm diameter have provided.
To ensure the characteristic strength, fy of the reinforcing bar, tensile strength
test were conducted using the universal testing machine as shown in Figure 3.3.
3.1.5
Formwork
Sets of formwork were prepared by using 12mm thickness plywood, 1 inch
by 2 inch timber and 2 inch by 3 inch timber and fabricated according to the size of
specimens required.
3.2
Preparation of Beam Specimens
Eight rectangular beams of 125mm in width, 150 in depth and 1400mm in
length were cast. The entire beams are grade 60 and two each with a different
percentage of MK7003. Main reinforcement are 16mm diameter high tensile steel
and cover is 25mm for all beams. For the 6mm shear link an 80mm spacing centre to
centre of legs link has used. The same reinforcements are used for all beams. Figure
3.2 has shown the detail of beam.
36
A pan mixer machine is used to produce the concrete mix. A vibration poker
is used to compact the concrete mix in the mould. The curing process was done by
using wet sack and water used daily to ensure the sack is under wet condition for 28
days. The above process are shown in Figure 3.4, Figure 3.5 and Figure 3.6.
3.3
Experimental Set Up
3.3.1
Strain Gauge
For each beam two strain gauges were used during carried out the testing. To
ensure the accurate result the concrete surface were cleaned by sand paper before
strain gauge stucked onto the selected location of beam. Electrical strain gauges
were mounted as shown in Figure 3.7 and Figure 3.8.
3.3.2
Testing Equipment
Beam specimens are tested in the structural laboratory of Faculty of Civil
Engineering UiTM Pulau Pinang. The testing equipment consist of:
i)
Universal Testing Machine 1000KN connected with data logger and
internal load cell.
ii)
Strain gauge with gauge length 67mm (two number for each specimen)
iii)
External transducer to measured deflection at mid span
iv)
Dial gauge to measured deflection at mid span.
Test set up has shown in Figure 3.9 and Figure 3.10.
37
3.3.3
Static Loading
This testing is to observe serviceability and ultimate behaviour of beam
specimen. The beam specimens were subjected to four points loading (Figure 3.2)
and loaded with static loading until failure and carefully studied are important to
determine the mode of failure. Load is applied in 5kN interval of increment.
Monitoring of deflection by placing transducer and dial gauge at the mid
span of beam as shown in Figure 3.11.
The occurrence of crack are checked by naked eye and further check the
crack mouth opening displacement and crack length by using hand held microscope
and steel ruler as shown in Figure 3.12. All reading of strains from the gauges and
mid span deflections is recorded by data logger.
38
Figure 3.1 : Metakaolin (MK7003)
P/2
550
P/2
300
550
x
R6 – 80 c/c
100
x
100
2R6
R6-80 c/c
2T16
Section x - x
Figure 3.2 : Beam Size and Reinforcement Detail
39
Figure 3.3 : Tensile Test
Figure 3.4 : Concrete Mix
40
Figure 3.5 : Compaction Process
Figure 3.6 : Curing Process
41
Figure 3.7 : Strain gauge location
x
120mm
700mm
x
Section x - x
= strain gauge
Figure 3.8 : Diagram of strain gauge location
42
Figure 3.9 : Test set up
Load Cell
Beam specimen
Strain gauge
Tranduser
Data Logger
Figure 3.10 : Diagram of test set up
43
Figure 3.11 : Deflection measurement by tranduser
Figure 3.12 : Crack measurement by microscope
44
CHAPTER 4
RESULT, ANALYSIS AND DISCUSSION
4.1
Results
4.1.1
Preliminary Testing
These preliminary tests are included compressive strength tests for concrete
cube and tensile strength test for steel. They were done to ensure the materials used
achieved limit state requirement as stated in BS 8110.
4.1.1.1 Concrete Mixed Design and Trial Mix for Grade 60
The purpose of a concrete mix design is to have economical mix proportions
for the available concreting materials which complies with the required compressive
strength of this research and has adequate workability to be placed in formwork.
Appendix A was shown the concrete mixed design for grade 60.
45
The MK7003 used in the mix are by using replacement method, from
5%,10% and 15%. The percentage of MK7003 is replacement to cement content in
term of weight.
The determining concrete strength for trial mix, 150mm cubes of concrete
are cast, cured and compressed for 7 and 28 days using compression machine.
Compressive strength test result for each beam is shown in Table 4.1. From
the results obtained, beam with 10% replacement by MK7003 achieved high
compressive strength 68.05 KN/mm2. This result has show the increment of 8.9% of
compressive strength compare to control sample.
4.1.1.2 Reinforcement Tensile Test
Tensile test result has shown in Table 4.2, that the characteristic strength of
the reinforcement has been used according to the limit state. It can be seen for high
yield bar with diameter 16mm achieved higher value of yield stress compare to
proof stress, 460 N/mm2.
4.1.2
Static Loading Test Results
The structure behaviour observations were made onto those beams including:
i)
Load increment and ultimate load
ii)
Strain reading
iii)
Deflection at mid span
iv)
Initial crack occur and crack width
v)
Type of crack failure
46
4.1.2.1 Experimental Reading
The data were recorded by data logger and manually. Load increment and
ultimate load, strain reading, deflection at mid span are recorded by data logger. The
crack width and crack length are attempt to record manually but very difficult to
measure using hand held microscope and no results for this parameter from
experiment. The readings recorded are shown in Table 4.3.
4.2
Analysis & Discussion
Before further analysis is made, the raw data obtained in the experiment are
analysis in order to determine the following parameter:
i)
Bending Moment corresponding to each load
ii)
Bending stress corresponding to each load
iii)
Average strain corresponding to each load
iv)
Theoretical deflection
v)
Theoretical load for initial crack
The overall results of the computation are as shown in Table 4.4 (a – d), Table 4.5
and Table 4.6.
4.2.1
Ultimate Moment Resistance of the Beam
The theoretical values of ultimate moment resistance or moment capacity of
the beam are calculated by using analysis of the section and sample calculation is
shown in Appendix B.
47
Table 4.7 has show the theoretical and experimental value of the ultimate moment
resistance. From the results, it shown that the increment of the moment resistance for
all beams with MK 7003 in range of 3 – 9% and beam with 10% MK7003 has
highest moment resistance about 26.33 kNm compared to control sample is about
24.08 kNm.
4.2.2
Stress and Strain Relationship
After the results were obtained from raw data analyses, stress strain
relationship of the beam are plotted and the static modulus of elasticity of the beam
are obtained from linear part of the graph as shown in Figure 4.1(a - d).
The modulus of elasticity, Ec can be related to the cube compressive strength
as a theoretical value by the expression in SI unit, Ec = 5.5 (fcu /1.5)0.5. The
experimental and theoretical values of Ec are shown in Table 4.8. The sample
calculation for theoretical modulus of elasticity has shown in Appendic C .
4.2.3
Deflection Behaviour
The theoretical values of deflection are analyse based on Mac Caulay
method. Sample calculations are shown in Appendix D.
The experimental and theoretical deflection values in Table 4.5, show the
different values respective to percentage (%) of MK7003 contents. Figure 4.2 has
show the theoretical and experimental deflection at various loading of beams.
48
From experimental reading, at load 95 kN as example, it can be seen that the
beam with 10% MK7003 deflect less, about 8.25mm compared to others percentage
of MK7003, which beam with 5% MK7003 shown the more deflection around
9.1mm but still less compared to control sample (0% MK7003) with deflection
9.5mm. The deflections at ultimate load for all beams have shown that with 10%
Mk7003 beam capable to resist more deflection before collapse. The collapse
deflection for beam with 10%MK7003 is 16.1mm and the less deflection resistance
is beam with 5% MK7003 about 14.9mm but still higher than control sample (0%
MK7003) is about 14.9mm. From that, can be seen the relationship of the deflection
with the modulus of elasticity, which the beam with high modulus of elasticity will
show the less deflection.
It was observed from Table 4.5, that the calculated deflection using Mac
Caulay method could not properly approximate the experimental deflection. It will
be retested future to confirm the deflection values, where considerably higher
deflection values were noted as compared to theory.
The deflection almost linearly increased for these beams. Deflection mainly
depends on the stiffness of the beam, so the stiffness of the beam is reduced as the
vertical deformation increased.
4.2.4
Crack Behaviour
All the beams, the first crack or initial crack which observed by naked eye
were noticed to occur in the middle of the span which is the region of the maximum
bending moment as shown in Figure 4.3.
Table 4.6 has shown the theoretical and experimental initial cracks occur and
respective load. The theoretical values of load are based on tensile strength of
concrete, which about 10% of the concrete compressive strength. It shown that beam
with 10% of MK7003 can resist more loads about 20kN before initial crack occurred
49
at middle part of beam span. For other beams including the control sample the initial
crack occur at load about 15kN.
The numbers of crack at middle span were seen to increase with the load.
Once the loads reach about 40kN – 50kN, shear crack start to occur for all beams.
This shear crack occur between point load and support for both side of beams. Then
the shear cracks propagate at a faster rate compared to bending crack and finally
from the Figure 4.4 and Figure 4.5 shown the location and pattern of crack occurred
at ultimate load. It showed a flexure-shear crack failure in the loaded zone for all
sample of beams. This failure is caused by the interaction of bending cracks and
diagonal cracks due to the diffusion of the concentrated load.
50
Table 4.1 : Average Compressive Strength at Various MK7003 Contents
MK7003 Contents
(%)
Average Concrete Cube Compressive Strength
( N/mm2 )
7 Days
28 Days
0
55.45
62.48
5
58.1
64.04
10
60.75
68.05
15
55.12
64.85
Table 4.2 : Tensile Test Result
Reinforcement
T16
Diameter (mm)
15.85
Area ( mm2 )
197.31
Gauge Length (mm)
Before
248
After
280
Yield Load (kN)
112
Ultimate Load (kN)
134
Breaking Load (kN)
91
Yield Stress (N/mm2 )
568
51
Table 4.3 : Data From Experimental Reading
Load
(kN)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
96
Strain Gauge 1 Reading(10-6 )
Deflection(mm)
0%MK 5%MK 10%MK
0
0
0
0.15
0.12
0.1
0.35
0.3
0.25
0.75
0.73
0.7
1.1
1.04
0.95
1.52
1.41
1.3
1.93
1.83
1.6
2.39
2.26
2.01
2.83
2.62
2.42
3.45
3.24
3.01
3.75
3.54
3.25
4.18
3.97
3.64
4.59
4.46
4.17
5.13
5.07
4.97
5.79
5.62
5.47
6.27
6.11
5.89
7.02
6.72
6.58
7.38
7.27
6.81
8.5
8.43
7.61
9.5
9.1
8.25
9.9
8.45
15%MK
0
0.15
0.29
0.75
1.03
1.38
1.8
2.22
2.54
3.18
3.34
3.81
4.32
5.06
5.5
6.05
6.68
7.04
8.04
8.91
-
0%MK
8
40
97
149
202
284
339
382
409
477
543
565
624
687
732
835
932
1052
1238
1460
1518
Strain Gauge 2 Reading(10-6 )
5%MK 10%MK 15%MK 0%MK
5
3
6
7
65
52
62
45
110
102
104
99
137
132
133
150
214
186
206
199
259
215
260
279
304
262
309
325
352
305
345
367
409
349
398
403
462
392
453
472
501
445
494
535
558
497
534
559
612
544
585
630
673
595
649
675
732
647
718
724
832
755
813
828
925
817
918
923
1097
1005
1065
1043
1232
1112
1219
1224
1460
1287
1367
1450
1513
5%MK 10%MK 15%MK
4
3
10
68
55
63
108
105
109
135
130
137
210
183
202
247
210
250
300
255
314
356
300
354
415
351
416
454
388
455
497
449
497
547
491
548
600
541
590
666
591
638
725
640
723
821
750
801
928
825
904
1080
985
1070
1225
1101
1197
1458
1263
1362
-
52
Table 4.3 (continue)
99
10.38
94
14.6
14.9
100
97
105
102
-
9
9.2
10.5
16.1
9.6
15.5
-
1545
-
1569
1590
-
-
1383
1473
1595
1497
1570
-
1527
-
1549
1590
-
-
1386
1480
1587
1499
1572
-
53
Table 4.4(a) : Average strain, bending moment and bending stress for 0%MK7003
Load
( kN )
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
96
94
Strain Gauge Reading
0% MK7003 ( 10-6 )
Gauge 1
8
40
97
149
202
284
339
382
409
477
543
565
624
687
732
835
932
1052
1238
1460
1518
1545
Gauge 2
7
45
99
150
199
279
325
367
403
472
535
559
630
675
724
828
923
1043
1224
1450
1513
1527
Average
7.5
42.5
98.0
149.5
200.5
281.5
332.0
374.5
406.0
474.5
539.0
562.0
627.0
681.0
728.0
831.5
927.5
1047.5
1231.0
1455.0
1515.5
1536.0
Bending
Moment,
(kNm)
Bending Stress
(N/mm2 )
0.07875
1.32875
2.57875
3.82875
5.07875
6.32875
7.57875
8.82875
10.07875
11.32875
12.57875
13.82875
15.07875
16.32875
17.57875
18.82875
20.07875
21.32875
22.57875
23.82875
24.07875
23.57875
0.1008
1.7008
3.3008
4.9008
6.5008
8.1008
9.7008
11.3008
12.9008
14.5008
16.1008
17.7008
19.3008
20.9008
22.5008
24.1008
25.7008
27.3008
28.9008
30.5008
30.8208
30.1808
54
Table 4.4 (b) : Average strain, bending moment and bending stress for 5%MK7003
Load
( kN )
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
99
94
Strain Gauge Reading
5% MK7003 ( 10-6 )
Gauge 1
5
65
110
137
214
259
304
352
409
462
501
558
612
673
732
832
925
1097
1232
1460
1569
1590
Gauge 2
4
68
108
135
210
247
300
356
415
454
497
547
600
666
725
821
928
1080
1225
1458
1549
1598
Average
4.5
66.5
109.0
136.0
212.0
253.0
302.0
354.0
412.0
458.0
499.0
552.5
606.0
669.5
728.5
826.5
926.5
1088.5
1228.5
1459.0
1559.0
1594.0
Bending
Moment,
( kNm)
Bending Stress
(N/mm2 )
0.07875
1.32875
2.57875
3.82875
5.07875
6.32875
7.57875
8.82875
10.07875
11.32875
12.57875
13.82875
15.07875
16.32875
17.57875
18.82875
20.07875
21.32875
22.57875
23.82875
24.82875
23.57875
0.1008
1.7008
3.3008
4.9008
6.5008
8.1008
9.7008
11.3008
12.9008
14.5008
16.1008
17.7008
19.3008
20.9008
22.5008
24.1008
25.7008
27.3008
28.9008
30.5008
31.7808
30.1808
55
Table 4.4 (c):Average strain, bending moment and bending stress for 10% MK7003
Load
( kN )
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
102
Strain Gauge Reading
10% MK7003 ( 10-6 )
Gauge 1
3
52
102
132
186
215
262
305
349
392
445
497
544
595
647
755
817
1005
1112
1287
1383
1473
1595
Gauge 2
3
55
105
130
183
210
255
300
351
388
449
491
541
591
640
750
825
985
1101
1263
1386
1480
1587
Average
3.0
53.5
103.5
131.0
184.5
212.5
258.5
302.5
350.0
390.0
447.0
494.0
542.5
593.0
643.5
752.5
821.0
995.0
1106.5
1275.0
1384.5
1476.5
1591.0
Bending
Moment,
( kNm)
Bending Stress
(N/mm2 )
0.07875
1.32875
2.57875
3.82875
5.07875
6.32875
7.57875
8.82875
10.07875
11.32875
12.57875
13.82875
15.07875
16.32875
17.57875
18.82875
20.07875
21.32875
22.57875
23.82875
25.07875
26.32875
25.57875
0.1008
1.7008
3.3008
4.9008
6.5008
8.1008
9.7008
11.3008
12.9008
14.5008
16.1008
17.7008
19.3008
20.9008
22.5008
24.1008
25.7008
27.3008
28.9008
30.5008
32.1008
33.7008
32.7408
56
Table 4.4 (d) : Average strain, bending moment and bending stress for 15% MK7003
Load
( kN )
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
97
Strain Gauge Reading
15% MK7003 ( 10-6 )
Gauge 1
6
62
104
133
206
260
309
345
398
453
494
534
585
649
718
813
918
1065
1219
1367
1497
1570
Gauge 2
10
63
109
137
202
250
314
354
416
455
497
548
590
638
723
801
904
1070
1197
1362
1499
1572
Average
8.0
62.5
106.5
135.0
204.0
255.0
311.5
349.5
407.0
454.0
495.5
541.0
587.5
643.5
720.5
807.0
911.0
1067.5
1208.0
1364.5
1523.0
1571.0
Bending
Moment
( kNm)
Bending Stress
(N/mm2 )
0.07875
1.32875
2.57875
3.82875
5.07875
6.32875
7.57875
8.82875
10.07875
11.32875
12.57875
13.82875
15.07875
16.32875
17.57875
18.82875
20.07875
21.32875
22.57875
23.82875
25.07875
24.32875
0.1008
1.7008
3.3008
4.9008
6.5008
8.1008
9.7008
11.3008
12.9008
14.5008
16.1008
17.7008
19.3008
20.9008
22.5008
24.1008
25.7008
27.3008
28.9008
305008
32.1008
31.1408
57
Table 4.5 : Theoretical and Experimental Load Versus Deflection
Load
kN
Replacement 0%MK
Exp
MacCaulay
(mm)
(mm)
Replacement 5%MK
Exp
MacCaulay
(mm)
(mm)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
0.00
0.15
0.35
0.75
1.10
1.52
1.93
2.39
2.83
3.45
3.75
4.18
4.59
5.13
5.79
6.27
7.02
7.38
8.50
0.00
0.12
0.30
0.73
1.04
1.41
1.83
2.26
2.62
3.24
3.54
3.97
4.46
5.07
5.62
6.11
6.72
7.27
8.43
0.00
0.15
0.31
0.46
0.62
0.77
0.92
1.08
1.23
1.38
1.54
1.69
1.85
2.00
2.15
2.31
2.46
2.62
2.77
0.00
0.15
0.29
0.44
0.58
0.73
0.88
1.02
1.17
1.31
1.46
1.60
1.75
1.90
2.04
2.19
2.33
2.48
2.63
Replacement 10%MK
Exp
MacCaulay
(mm)
(mm)
0.00
0.10
0.25
0.70
0.95
1.30
1.60
2.01
2.42
3.01
3.25
3.64
4.17
4.97
5.47
5.89
6.58
6.81
7.61
0.00
0.13
0.26
0.38
0.51
0.64
0.77
0.89
1.02
1.15
1.28
1.40
1.53
1.66
1.79
1.91
2.04
2.17
2.30
Replacement 15%MK
Exp
MacCaulay
(mm)
(mm)
0.00
0.15
0.29
0.75
1.03
1.38
1.80
2.22
2.54
3.18
3.34
3.81
4.32
5.06
5.50
6.05
6.68
7.04
8.04
0.00
0.14
0.29
0.43
0.58
0.72
0.86
1.01
1.15
1.29
1.44
1.58
1.73
1.87
2.01
2.16
2.30
2.45
2.59
58
Table 4.5 (continue)
95
9.50
96
9.90
99
94
14.60
100
97
105
102
-
2.92
2.95
-
2.89
-
9.10
10.38
14.90
2.77
-
-
-
-
-
-
-
-
2.89
2.74
8.25
8.45
9.00
9.20
10.50
16.10
2.42
2.45
2.53
-
2.55
-
2.68
2.60
8.91
9.60
15.50
2.73
-
-
-
-
-
2.88
2.79
59
Table 4.6 : Initial Crack Load
Specimen
0%mk7003
5%mk7003
10%mk7003
15%mk7003
Theory
kN
6.2
6.4
6.8
6.5
Experiment
kN
15
15
20
15
Table 4.7 : Theoretical and Experimental Ultimate Moment Resistance
Specimen
0%mk7003
5%mk7003
10%mk7003
15%mk7003
Theory
kNm
17.14
17.22
17.40
17.25
Experiment
kNm
24.08
24.83
26.33
25.08
Table 4.8 : Theoretical and Experimental Modulus of Elasticity
Specimen
Theoretical
kN/mm2
Experimental
kN/mm2
0% MK 7003
35.5
30.41
5% MK 7003
35.94
32.07
10% MK 7003
37.05
36.69
15% MK 7003
36.16
32.52
60
Stress Versus Strain (0%MK7003)
0.035
0.03
stress (KN/mm^2)
0.025
0.02
0% MK7003
Ec = 30.41KN/mm^2
0.015
0.01
0.005
0
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
1800.0
strain ( 10^-6)
Figure 4.1 (a) – Stress strain relationship 0% MK7003
Stress versus Strain (5%MK7003)
0.035
0.03
stress(KN/mm^2)
0.025
0.02
5% MK7003
0.015
Ec = 32.07KN/mm^2
0.01
0.005
0
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
strain (10^-6)
Figure 4.1 (b) – Stress strain relationship 5% MK 7003
1800.0
61
Stress versus Strain (10% MK7003)
0.04
0.035
0.025
0.02
10% MK7003
Ec = 34.14KN/mm^2
0.015
0.01
0.005
0
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
1800.0
Strain (10^-6)
Figure 4.1 ( c) – Stress strain relationship 10% MK 7003
Stress Versus Strain (15%MK7003)
0.035
0.03
0.025
Stress (KN/mm^2)
stress (KN/mm^2)
0.03
0.02
15%MK7003
Ec = 32.52KN/mm^2
0.015
0.01
0.005
0
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
1600.0
1800.0
Strain (10^-6)
Figure 4.1 ( d ) – Stress strain relationship 15% MK 7003
62
Load versus Theoretical and Experimental Deflection
120
100
80
0%mk7003 exp
Load (KN)
5%mk7003 exp
10%mk7003 exp
15%mk7003 exp
60
0%mk7003 theory
5%mk7003 theory
10%mk7003 theory
15%mk7003 theory
40
20
0
0
2
4
6
8
10
12
14
16
18
Deflection (mm)
Figure 4.2 – Load versus theoretical and experimental deflection
Figure 4.3 – Initial crack occur at middle span.
63
Figure 4.4 – Location and pattern of crack at failure
Figure 4.5 : Location and pattern of crack.
64
CHAPTER 5
CONCLUSION AND RECOMMENDATION
5.1
Conclusion
The following conclusions can be drawn from the results and analysis of this study:
i)
It was observed that the calculated deflection using double integration
method (Macaulay Method) could not properly approximate the
experimental deflection. It will be retested future to confirm the
deflection values, where considerably higher deflection values were
noted as compared to theory. Beam with 10% of MK7003 able to resist
more deflection before failure which is about 16.1mm and 10.3% higher
than control sample.
ii)
The initial crack of all MK7003 beams occurred at load 15 to 20 kN
compared to 6.4 kN to 6.8 kN estimated by theory. It may due to
difficulty to detect the microcrack by naked eye. From tested beams
shows the 10% MK7003 beam able to resist more load about 20KN and
30% higher than control sample before initial crack noticed to occur.
65
iii)
All beam have shown, with the shear span over effective depth ratio
equal to 3.6, the crack at failure for all beams are flexure-shear failure
(Figure 4.4).
iv)
The beam with MK7003 able to resist higher ultimate moment resistant
compare to control sample and with 10% replacement has highest
capability to resist 26.33 kNm ultimate moment resistance. It is 9.5%
higher than control sample.
v)
Modulus of elasticity of the beam with MK not much different compared
to BS8110. The experimental values in range of 32 kN/mm2 to 37
kN/mm2 for all beams and typical range from BS 8110 are 26 kN/mm2 to
38 kN/mm2.
5.2
Recommendation
i)
The experiment to study the crack propagation and to monitor the crack
mouth opening displacement (CMOD) should carry out with lower rate
of load.
ii)
The same experiment but with normal concrete strength should be carried
out, it may show the different results.
iii)
To study the structure behaviour of beam with fibers such as natural fiber
and steel fiber.
iv)
To study the bending and shear failure of the beam.
66
REFERENCES
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New Generation Mineral Admixture. Concrete Institute : 37 – 40.
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Repeated Loading and Fatique; University Malaya: Master Thesis
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Naville,A.M.(1987). Properties of Concrete; Longman
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68
APPENDIX A
Calculation Concrete Mix Design Grade 60
Stage 1
1.2 Standard deviation
1.3 Margin (k=1.96)
1.4 Target mean strength
1.5 Cement type
1.6 Coarse aggregate
Fine aggregate
1.7 Free water cement ratio
60N/mm2 at 28 days
Prop. Defective = 5%
8 N/mm2
1.96 x 8 = 15.68 N/mm2
60 + 15.68 = 75.68 N/mm2
OPC
Crushed
Uncrushed
0.35
2.1 Slump
2.2 Maximum aggregate size
2.3 Free water content
10 – 30 mm
20mm
190 kg/m3
3.1 Cement content
543 kg/m3
4.1 SSD
4.2 Concrete density
4.3 Total aggregate content
2.7 (assumed)
2430 kg/m3
1697 kg/m3
5.1 Grading of fine aggregate
5.2 Proportion of fine aggregate
5.3 Fine aggregate content
5.4 Coarse aggregate content
Passing 600 um = 40%
33 %
0.33 x 1697 = 560 kg/m3
1697 – 560 = 1137 kg/m3
1.1 Characteristic strength
Stage 2
Stage 3
Stage 4
Stage 5
Quantities
Cement (kg) Water(kg)
Agg
Per m3 (nearest 5kg)
545
190
Fine Agg
560
Coarse
1137
69
APPENDIX B
Sample calculation for ultimate moment resistance.
( Calculation are based on beam with 10% MK 7003)
Analysis of Doubly Reinforced Rectangular Section
568 N/mm2
Reinforcement strength, fy
68.05 N/mm2
Concrete strength , fcu
For equilibrium of the tensile and compressive forces on the section;
Fst = Fcc + Fsc
Assuming initially that the steel stresses are the design yield values, then
0.95fyAs = 0.45fcubs + 0.95fyA's
Fsc
Fcc
Fs
s =
x=
x/d =
d'/x =
42.9574
47.7304
0.40795
0.58663
d=150-25-8 = 117
d'=25+3 = 28
Moment about tension steel, M;
M=
17401473
17.40
N.mm
KNm
P
P
M
Ultimate applied force, P ;
P=
77.34
KN
P
P
70
APPENDIX C
Sample calculations for modulus of elasticity and initial crack theory.
(Calculations are based on beam with 10% Mk7003).
Cross section area, A
= 125mm x 150mm
= 18750 mm2
Moment of Inertia, Ixx
= (bd3)/12
= (125)(150)3/(12)
= 35156250 mm4
Modulus of Elasticity Theory, E
= 5.5 ( fcu/ 1.5)0.5
= 5.5 ( 68.05 / 1.5) 0.5
= 37.04 kN/mm2
Initial Crack Theory
= 10% (fcu)
= 0.1 (68.05)
= 6.85 N/mm2
71
APPENDIX D
Sample calculation for deflection theory by Macaulay Method.
(Calculations are based on beam with 10% Mk7003).
P/2
P/2
450
P/2
300
450
P/2
Bending moment equation at very right section, where x from left end.
Mx = P/2 (x) – P/2 ( x – 450 ) – P/2 (x – 750)
From elastic curve equation;
EI ( d2y/dx2) = Mx
EI ( dy/dx) = (P/2)(x2/2) – (P/2)(x -450)2/2 – (P/2)( x – 750)2/2 + A
EI ( y ) = (P/2)(x3/6) – (P/2)(x -450)3/6 – (P/2)( x – 750)3/6 + Ax + B
Boundary condition;
x=0;y=0
So, B = 0
And, x = 1200; y = 0
A = - 84375 P
Deflection equation, y;
y (EI) = Px3/12 – P (x – 450)3/12 – P(x – 750)3/12 – 84375 Px
Deflection maximum at mid span, x = 600 mm
E = 37.05 kN/mm2
I = 35156250 mm4
72
EI = 1302539063
y = P (600)3/12 – P(600 – 450)3/12 – 84375 P (600)
= - (32906250 P)/EI
For maximum deflection at maximum load, P = 105
y = - 32906250 (105)/ 1302539063
= - 2.65 mm
Maximum deflection at mid span = 2.65 mm (downward)