CHAPTER I
REINFORCED CONCRETE
1.1. BASIC CONCEPT OF REINFORCED CONCRETE
Although concrete is used very extensively in the construction of
buildings, bridges and many other engineering structures, its
mechanicals properties are far from ideal or not so perfect. For example,
it is not a particularly or predominantly strong material. The compressive
strength of structural grade concrete ranges typically or normally from 20
to 40 Mpa - 1MPa = 106 N/m² =1N/mm² = 0.10197 kgf/mm² -.
MPa is a metric (SI) unit for pressure, or force per unit area. Pa is the Pascal, which is
one Newton of force applied to one square meter of area (1 N/m2). MPa is a megaPascal, or one million Pascals. Since atmospheric pressure is 101 000 pA, or 101 kPa
(approximately 14.7 psi), this is approximately 9 atmospheres (around 150 psi).
Conversion from SI to Imperial or MKS Units
Megapascal (meganewton per square meter)
1 Mpa = 145.04 lbf/sq in
= 0.145 psi
= 20.885 ksf
= 9.32 ton/sq ft
(= 10.197 kgf/cm²)
(= 10 bar)
= N/mm²
NB: MKS unit is a metric system of units based on the metre, kilogram, and second: it forms
the basis of the SI units.
Units of mass
There are several similar units of mass or volume called the ton:
Full name
Common
name
long ton,
weight ton, "ton" (UK)
gross ton
Quantity
Notes
2240 pounds
(1016.0469088 kg)
Used in countries such as United Kingdom
that formerly used the Imperial system
1
short ton, net
"ton" (US)
ton
2000 lb
Used in North America
1000 kg
In UK and areas that used Imperial system,
metric ton is the form of ton legal form of
trade. Conveniently is less than 2%
difference from long ton.
ton short
weight
2240 lb
Used in the iron industry in the 17th
century and 18th centuries.
ton long
weight
2400 lb
Used in the iron industry in the 17th
century and 18th centuries. The
hundredweight was 120 lb.[1]
metric
ton,tonne
"metric
ton"
CHAPTER IV
FLEXURAL STRENGTH THEORY
4.1. OVERLOAD BEHAVIOUR IN FLEXURE
We first consider qualitatively the behavior of a beam which after
manufacture is cured for a period and is later subjected to a
gradually increasing bending moment M. The beam has a
rectangular section, and contains only tensile reinforcement of
area Ast at depth d, as shown in figure in Fig 4.1.
ε₀
d
C
M
Tc
Ast   
Ts
Strain
b
Figure 4.1. Uncracked member
2
Stress
Forces
SOME NOTES OF SYMBOLS WRITTEN ABOVE:
 Ast = area of tensile steel reinforcement.
 b = width of a rectangular cross section; or total width of the
compressive face in an I or T section.
 C = compressive force or column cross-section; or St. Venant
torsion constant for the cross section of a beam (chapter 14).
 d = effective depth (depth to tensile steel) for a cross-section.
 M = bending moment.
 T = tensile force; or torsion.
 Tc = tensile force of concrete.
 Ts = tensile force of steel.
 ε₀ = strain at extreme compressive face of cross-section in
bending or combined bending and compression.

= concrete stress at extreme compressive face.
SOME CONCISE THEORIES ABOUT:
 Strain in Mechanics is a force tending to pull or stretch something to an
extreme or damaging degree. Strain or deformation is the change in
shape of a body caused by an external loading In Physics is the
magnitude of a deformation, equal to the change in the dimension of a
deformed object divided by its original dimension. When a metal is
subjected to a load (force), it is distorted or deformed, no matter how
strong the metal or light the load. If the load is small, the distortion will
probably disappear when the load is removed. The intensity, or degree,
of distortion is known as strain. If the distortion disappears and the
metal returns to its original dimensions upon removal of the load, the
strain is called elastic strain. If the distortion disappears and the metal
remains distorted, the strain type is called plastic strain.
 Stress is the internal resistance, or counterforce, of a material to the
distorting effects of an external force or load. These counter forces
tend to return the atoms to their normal positions. The total resistance
developed is equal to the external load. This resistance is known as
stress.
GOOGLE SEARCH
Compressive and Tensile Force
1. Basic Types of Stresses, Tensile Stress, Compressive Stress and
Shear Stress.
http://www.eduresourcecollection.com/civil_sm_Stresses.php
[Online] (Accessed on 22/02/09)
3
Strength of Materials – Stress
Stresses
Stress is defined as the internal resistance set up by a body when it is deformed. It is
measured in N/m2 and this unit is specifically called Pascal (Pa). A bigger unit of stress
is the mega Pascal (MPa).
1 Pa = 1N/m2,
1MPa = 106 N/m2 =1N/mm2.
Three Basic Types of Stresses
Basically three different types of stresses can be identified. These are related to the
nature of the deforming force applied on the body. That is, whether they are tensile,
compressive or shearing.
Tensile Stress
Consider a uniform bar of cross sectional area A subjected to an axial tensile
force P. The stress at any section x-x normal to the line of action of the tensile
force P is specifically called tensile stress pt. Since internal resistance R at x-x is
equal to the applied force P, we have, pt = (internal resistance at x-x) / (resisting
area at x-x) =R/A=P/A.
Under tensile stress the bar suffers stretching or elongation.
Compressive Stress
If the bar is subjected to axial compression instead of axial tension, the stress developed
at x-x is specifically called compressive stress pc.
pc =R/A
= P/A.
4
Under compressive stress the bar suffers shortening.
Shear Stress
Consider the section x-x of the rivet forming joint between two plates subjected to a
tensile force P as shown in figure.
The stresses set up at the section x-x acts along the surface of the section, that is,
along a direction tangential to the section. It is specifically called shear or
tangential stress at the section and is denoted by q.
q =R/A
=P/A.
Normal or Direct Stresses
When the stress acts at a section or normal to the plane of the section, it is called a
normal stress or a direct stress. It is a term used to mean both the tensile stress and the
compressive stress.
Simple and Pure Stresses
The three basic types of stresses are tensile, compressive and shear stresses. The stress
developed in a body is said to be simple tension, simple compression and simple shear
when the stress induced in the body is (a) single and (b) uniform. If the condition (a)
alone is satisfied, the stress is called pure tension or pure compression or pure shear, as
the case may be.
Volumetric Stress
Three mutually perpendicular like direct stresses of same intensity produced in a body
constitute a volumetric stress. For example consider a body in the shape of a cube
subjected equal normal pushes on all its six faces. It is now subjected to equal
compressive stresses p in all the three mutually perpendicular directions. The body is
now said to be subjected to a volumetric compressive stress p.
5
Volumetric stress produces a change in volume of the body without producing
any distortion to the shape of the body.
GOOGLE SEARCH
Solved Problem about Reinforced Concrete
2. Schaum's Outline of Theory and Problems of Reinforced Concrete
Design - Google Books Result.
http://books.google.com.au/books?id=UAakcDL2658C&pg=P
A102&lpg=PA102&dq=Solved+Problem+about+reinforced+co
ncrete&source=bl&ots=pyA1usNOfb&sig=gazSasXXOQQNNW
rCtVDqMKQqGc&hl=en&ei=4jiiSZTmOoGStQPvrY3NCQ&sa=X&oi=
book_result&resnum=1&ct=result
[Online] Accessed on 23/02/09
As the concrete hardens, it shrinks. The steel reinforcement bounded or
encircled to the concrete is subjected to a gradually increasing
compressive force equilibrated by concrete stresses which are mainly
tensile. The fibers in the upper or higher portion of the beam shorten
more than those adjacent to or next to the steel and the resulting strain
gradient or raised produce a downward deflection of the member prior to
or before the application of any external load. This shrinkage or
contraction warping i.e. bending out of shape can be of practical
significance if the member is slender or small; however, the shrinkage
stresses are usually ignored in the analysis and design of normal flexural
or bent members. They are not shown in figure 4.1.
6
u
C
k’d
Mu
l’
  
T
st
Forces
Strain
fsy
Stress
What is the definition of compressive force C?
A compressive force C is a force or pressure that attempts or seeks to flatten
or squeeze a material pushing at both ends.
What is the definition of tensile force T?
A tensile force T is a stretching force (tension) pulling at both ends of a
component or structure along its length.
At all stages/phases of loading the basic equilibrium requirements are that the
resultant compressive force C and tensile force T are equal in magnitude.
C=T
ULTIMATE MOMENT CALCULATION
Calculate the moment carrying capacity of a rectangular section, containing only
tensile reinforcement, with the following properties:
Fc’ = 30 Mpa
Fsy = 230 Mpa
b = 250
d = 350
7
Ast = 1800 mm
SOLUTION:
(a) Lever arm: l’ =
(c) Ultimate Moment = Mu
Here the resultant tensile forces in the concrete and steel, Tc and Ts, are
together equal to the resultant compressive force C, and these forces form an
internal couple equal to moment M so we have an external applied moment
formula as follow
The formula of applied Ultimate Moment:
Mu = T x l’
Mu = 414 x 317 = 1.31 x 10 exp.8 Nmm = 131,000,000Nmm
131,000,000Nmm to be reduced
to kNm is equal to
131,000,000Nmm  10 exp.3 x 1 meter x 1000 = 131 kNm
Question
Sir, please let me know the approximate total load (DL+LL) for a typical common 2-storey
family house of 100 m2 (e.g. .... KN/m2)
Answer
This will vary between 14-18 kN/m2 per floor for habitable spaces and about 12-14 kN/m2
for the roof, assuming all construction is in stone/block work and reinforced concrete. So
overall, for a 2-storey building plus roof, it will be a maximum of 18+18+14 = 50 kN/m2
time 100 equals 5000 kN or about 500 tonnes.
1. Structural Software Inc. Beam Strength
http://www.strucsoft.com/applets/BeamStrength.htm
[Online] (Accessed on 21/02/09)
2. reinforced concrete: Definition from Answers.com
8
http://www.answers.com/topic/reinforced-concrete
[Online] (Accessed on 21/02/09)
<http://www.ilpi.com/msds/ref/pressureunits.html>
9
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Pressure Unit Conversions
Definition
Pressure is a measure of the force against a surface.
Pressure is usually expressed as a force per unit area.
Here is a handy conversion calculator for some
common pressure terms. The definitions of each term
are in the following section.
Pressure Conversion Calculator
(Enter number on the left side; answer appears on the right
side)
10
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Additional Info
Many of the items you will find on an MSDS come in both English (U.S.
Customary System) and metric (International System or SI or cgs) units. The
metric system has been adopted by almost every country except the United
States. Even in the U.S., scientists and technical people use the metric system
because of its ease of use.
If you are unfamiliar with the terms used in these definitions, see our mass
unit and distance unit conversion pages.
Unit
Pounds per
square inch
(psi, PSI,
lb/in2, lb/sq
in)
Equivalent measurements, comments
Commonly used in the U.S., but not elsewhere. Normal
atmospheric pressure is 14.7 psi, which means that a
column of air one square inch in area rising from the
Earth's atmosphere to space weighs 14.7 pounds.
Atmosphere Normal atmospheric pressure is defined as 1 atmosphere.
(atm)
1 atm = 14.6956 psi = 760 torr.
Torr
(torr)
Based on the original Torricelli barometer design, one
atmosphere of pressure will force the column of mercury
(Hg) in a mercury barometer to a height of 760
millimeters. A pressure that causes the Hg column to rise
1 millimeter is called a torr (you may still see the term 1
mm Hg used; this has been replaced by the torr. "mm
Hg" is commonly used for blood pressure
measurements). 1 atm = 760 torr = 14.7 psi.
Bar
(bar)
The bar nearly identical to the atmosphere unit. One bar
= 750.062 torr = 0.9869 atm = 100,000 Pa.
There are 1,000 millibar in one bar. This unit is used by
meteorologists who find it easier to refer to atmospheric
Millibar
(mb or mbar) pressures without using decimals. One millibar = 0.001
bar = 0.750 torr = 100 Pa.
Pascal
(Pa)
Kilopascal
1 pascal = a force of 1 Newton per square meter (1
Newton = the force required to accelerate 1 kilogram one
meter per second per second = 1 kg.m/s2; this is actually
quite logical for physicists and engineers, honest). 1
pascal = 10 dyne/cm2 = 0.01 mbar. 1 atm = 101,325
Pascals = 760 mm Hg = 760 torr = 14.7 psi.
The prefix "kilo" means "1,000", so one kilopascal =
11
(kPa)
1,000 Pa. Therefore, 101.325 kPa = 1 atm = 760 torr and
100 kPa = 1 bar = 750 torr.
The prefix "mega" means "1,000,000", so one
Megapascal
megapascal = 1,000 kPa = 1,000,000 Pa = 9.869 atm =
(MPa)
145 psi.
Gigapascal
(GPa)
The prefix "giga" means "1,000,000,000", so one
gigapascal = 1,000 MPa = 1,000,000 kPa =
1,000,000,000 Pa = 9,870 atm = 10,000 bar. Pressures of
several gigapascals can convert graphite to diamond or
make hydrogen a metallic conductor! Such high
pressures are rarely encountered in everyday life.
MSDS Relevance
Be very careful to note the units when reading numbers on an MSDS. If you
ever perform a calculation of any sort, always remember to write the units next
to each number in your calculation and make sure that they cancel properly.
Further Reading
o
o
The U.S. Metric Program at the National Institute of Standards.
More info about the metric system, including prefixes, at ChemTeam.
See also: area units, distance units, mass units, energy units, mole, temperature units,
vapor pressure, volume units.
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