ELEMENTS OF RCC DESIGN
Q.1.
Write down the assumption of simple bending.
In
engineering mechanics
,
bending
(also known as
flexure
) charact
erizes the behavior of a
slender
structural
element subjected to an external
load
applied perpendicularly
to a
longitudinal axis
of the element.
The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or
less, of the
other two.
[1]
When the length is considerably longer than the width and the thickness, the element is called
a
beam
. A
closet
rod
sagging
under the weight of clothes on
clothes hangers
is an example of a beam experiencing
bending. On the other hand, a
shell
is a structure of any geometric form where the len
gth and the width are of the
same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large
diameter, but thin

walled, short tube supported at its ends and loaded laterally is an example of a shell experie
ncing
bending.
In the absence of a qualifier, the term
bending
is ambiguous because bending can occur locally in all objects. To
make the usage of the term more precise, engineers refer to the
bending of rods
,
[2]
the
bending of
beams
,
[1]
the
bending of plates
,
[3]
the
bending of shells
[2]
and so on.
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Quasistatic bending of beams
A beam deforms and stresses develop inside it when a transverse load is applied on it. In the quasist
atic case, the
amount of bending
deflection
and the stresses that develop are assumed not to change over time. In a horizontal
beam supported at the ends and l
oaded downwards in the middle, the material at the over

side of the beam is
compressed while the material at the underside is stretched. There are two forms of internal stresses caused by
lateral loads:
Shear stress
parallel to the lateral loading plus complementary shear stress on planes
perpendicular to the load direction;
Direct
compressive stress
in the upper region of the beam, and direct
tensile stress
in the lower
region of the beam.
These last two forces form a
couple
or
moment
as they are equal in magnitude and opposite in direction.
This
bending moment
resists the sagging deformation characteristic of a beam experiencing bending. The stress
distribution in a beam can be predicted quite accurately even when some simplifying assumptions are used.
[1]
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Euler

Bernoulli bending theory
Main article:
Euler

Bernoulli beam equation
Element of a bent beam: the fibers form conce
ntric arcs, the top fibers are compressed and bottom fibers stretched.
Bending moments in a beam
In the
Euler

Bernoulli theory
of slender beams, a major assumption is that 'plane sections remain plane
'. In other
words, any deformation due to shear across the section is not accounted for (no shear deformation). Also, this linear
distribution is only applicable if the maximum stress is less than the
yield stress
of the material. For stresses that
exceed yield, refer to article
plastic bending
. At yield, the maximum stress experienced in the section (at t
he furthest
points from the neutral axis of the beam) is defined as the
flexural strength
.
The Euler

Bernoulli equation for the quasistatic bending of slender, isotropic, h
omogeneous beams of constant cross

section under an applied transverse load
q
(
x
)
is
[1]
where
E
is the
Young's modulus
,
I
is the
area moment of inertia
of the cross

section, and
w
(
x
)
is the deflection
of the neutral axis of the beam.
After a solution for the
displacement of the beam has been obtained, the bending moment (
M
) and shear force
(
Q
) in the beam can be calculated using the relations
Simple beam bending is often analyzed with the Euler

Bernoulli beam equation. The conditions for using
simple bendin
g theory are
[4]
:
1.
The beam is subject to
pure bending
. This means that the
shear force
is zero, and that
no torsional or axial loads are present.
2.
The material is
isotropic
and
homogeneous
.
3.
The material obeys
Hooke's law
(it is linearly elastic and will not deform plastically).
4.
The beam is initially straight with a cross sect
ion that is constant throughout the beam
length.
5.
The beam has an axis of symmetry in the plane of bending.
6.
The proportions of the beam are such that it would fail by bending rather than by
crushing, wrinkling or sideways
buckling
.
7.
Cross

sections of the beam remain plane during bending.
Deflection of a beam deflected symmetrically and principle of su
perposition
Compressive and tensile forces develop in the direction of the beam axis under bending loads. These
forces induce
stresses
on the beam. The maximum compressive st
ress is found at the uppermost edge of
the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses
between these two opposing
maxima
vary
linearly
, there therefore exists a point on the linear path between
them where there is no bending stress. The
l
ocus
of these points is the neutral axis. Because of this area
with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a
particularly efficient means of supporting a load as it does not use the full capac
ity of the beam until it is on
the brink of collapse. Wide

flange beams (
I

beams
) and
truss
girders
effectively address this inefficiency
as they minimize the amount of material in this under

stressed region.
The classic formula for determining the bending stress in a beam under simple bending is
[5]
:
where
σ
is the bending stress
M

the moment about the
neutral axis
y

the perpendicular distance to the neutral axis
I
x

the
second moment of area
about the neutral axis
x
Q.2
Explain under reinforced section.
Reinforced concrete
is
concrete
in which reinforcement bars ("
rebars
"), reinforcement grids,
plates
or
fibers
have
been incorporated to strengthen the concrete in
tension
. It was i
nvented by
French
gardener
Joseph Monier
in 1849
and
pate
nted
in 1867.
[1]
The term Ferro Concrete refers only to concrete that is reinforced with iron or steel. Other
materials used to reinforce concrete can be organic and inorganic
fibres as well as
composites
in different forms.
Prior to the invention of reinforcement, concrete was strong in
compression
, but weak in tension. Adding
reinforcement crucially increases the strength in tension. The failure strain of concrete in tension is so low that the
reinforcement has to hold the cracked sections together
.
For a strong, ductile and durable construction the reinforcement needs to have the following properties:
High strength
High tensile strain
Good bond to the concrete
Thermal compatibility
Durability in the concrete environment
In most cases reinforced con
crete uses steel rebars that have been inserted to add strength.
Use in construction
Rebars of
Sagrada Família
's roof in construction (2009)
Concrete is reinforced to give it extra tensile strength; without reinforcement, many concrete buildings would not have
been possible.
Reinforced concrete can encompass many types of structur
es and components,
including
slabs
,
walls
,
beams
,
columns
,
foundations
,
frames
and more.
Reinforced concrete can be classified as
precast
or
cast in

situ concrete
.
Much of the focus on reinforcing concrete is placed on
floor
systems. Designing and implementing the most efficient
floor system is key to creating optimal building struc
tures. Small changes in the design of a floor system can have
significant impact on material costs, construction schedule, ultimate strength, operating costs, occupancy levels and
end use of a building.
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]
Behavior of reinforced concrete
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]
Materials
Concrete is a mixture of Coarse (stone or brick chips) and Fine (generally sand or crushed stone) aggregates with a
binder material(usually
Portland cement
)
. When mixed with a small amount of water, the cement
hydrates
to form
microscopic opaque crystal lattices encapsulating and locking the aggregate into a rigid structure. Typical concrete
mi
xes have high resistance to
compressive
stresses
(about 4,000
psi (28
MPa)); how
ever, any
appreciable
tension
(
e.g.,
due to
bending
) will break the microscopic rigid lattice, resulting
in cracking and separation
of the concrete. For this reason, typical non

reinforced concrete must be well supported to prevent the development
of tension.
If a material with high strength in tension, such as
steel
, is placed in concrete, then the composite
material,
reinforced concrete
, resists not only compression but also bending and other direct tensile actions. A
reinforced concrete section where the concrete resists the compression and steel
resists the tension can be made
into almost any shape and size for the construction industry.
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]
Key characteristics
Three physical characteristics give reinforced concrete its special properties.
First, the
coefficient of thermal expansion
of concrete is si
milar to that of steel, eliminating large internal stresses due
to differences in
thermal
expansion or contraction.
Second, when the cement paste within the concrete hardens this conforms to the surf
ace details of the steel,
permitting any stress to be transmitted efficiently between the different materials. Usually steel bars are roughened or
corrugated to further improve the
bond
or cohesion between the concrete and steel.
Third, the
alkaline
chemical environment provided by the
alkali
reserve (KOH, NaOH) and th
e
portlandite
(
calcium
hydroxide
) contained in the hardened cement paste causes a
passivating
film to form on the surface of the steel,
making it much more resistant to
corrosion
than it would be in neutral or ac
idic conditions. When the cement paste
exposed to the air and meteoric water reacts with the atmospheric CO
2
, portlandite and the
Calcium Silicate
Hydrate
(CS
H) of the hardened cement paste become progressively carbonated and the high pH gradually decreases
from 13.5
–
12.5 to 8.5, the pH of water in equilibrium with
calcite
(
calcium carbonate
) and the steel is no longer
passivated.
As a rule of thumb, only to give an idea on orders of magnitude, steel is protected at pH above ~11 but starts to
corrode below ~10 depe
nding on steel characteristics and local physico

chemical conditions when concrete becomes
carbonated.
Carbonation
of concrete along with
chloride
ingress are amongst the chief reasons for the failure
of
reinforcement bars
in concrete.
[2]
The relative cross

sectional
area
of steel required for typical reinforced concrete is usually quite small and varies from
1% for most beams and slabs to 6% for some colu
mns.
Reinforcing bars
are normally round in cross

section and vary
in diameter. Reinforced concrete structures sometimes have provisions such as ventilated hollow cores to control
their moisture &
humidity.
Distribution of concrete (in spite of reinforcement) strength characteristics along the cross

section of vertical
reinforced concrete elements is inhomogeneous.
[3]
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]
Mechanism of composite action of reinforcement and concrete
The reinforcem
ent in a RC structure, such as a steel bar, has to undergo the same strain or deformation as the
surrounding concrete in order to prevent discontinuity, slip or separation of the two materials under load. Maintaining
composite action requires transfer of l
oad between the concrete and steel. The direct stress is transferred from the
concrete to the bar interface so as to change the tensile stress in the reinforcing bar along its length. This load
transfer is achieved by means of bond (anchorage) and is ideal
ized as a continuous stress field that develops in the
vicinity of the steel

concrete interface.
Q.3
What is local band? Explain.
Q.4
What do you mean by contilenes beam.
Beams are made continuous over the supports to increase structural integrity. A
continuous beam provides an alternate load path in the case of failure at a section. In
regions with high seismic risk, continuous beams and frames are preferred in buildings
and bridges. A continuous beam is a statically indeterminate structure.
The
advantages of a continuous beam as compared to a simply supported beam are as
follows.
1) For the same span and section, vertical load capacity is more.
2) Mid span deflection is less.
3) The depth at a section can be less than a simply supported beam
for the same
span. Else, for the same depth the span can be more than a simply supported
beam.
⇒
The continuous beam is economical in material.
4) There is redundancy in load path.
⇒
Possibility of formation of hinges in case of an extreme event.
5) Requires less number of anchorages of tendons.
6) For bridges, the number of deck joints and bear
ings are reduced.
⇒
Reduced maintenance
There are of course several disadvantages of a continuous beam as compared to a
simply supported beam.
1) Difficult analysis and design procedures.
2) Difficulties in construction, especially for precast member
s.
3) Increased frictional loss due to changes of curvature in the tendon profile.
4) Increased shortening of beam, leading to lateral force on the supporting columns.
5) Secondary stresses develop due to time dependent effects like creep and
shrinkage
, settlement of support and variation of temperature. Prestressed Concrete Structures
Dr. Amlan K Sengupta and Prof. Devdas Menon
Indian Institute of Technology Madras
6) The concurrence of maximum moment and shear near the supports needs
proper det
ailing of reinforcement.
7) Reversal of moments due to seismic force requires proper analysis and design.
Q.5
How will you design a one

way slab?
Q.6
What is RC column?
FOOTING AND FOOTING REINFORCE

MENT.
—
Footings
support
the
entire
structure
and
distribute
the
load
to
the
ground.
The
size
and
shape
of
a
footing
depend
upon
the
design
of
the
structure.
In
a
small
footing
(fig.
7

2),
“steel
mats”
o
r
reinforcements
are
generally
preassembled
and
placed
after
the
forms
have
been set. In
large or continuous footings, such as
those found under bearing walls,
steel mats are
constructed
in
place.
COLUMN
AND
COLUMN
REINFORCE

MENT.
—
A
column
i
s
a
slender,
vertical
member
that
carries
a
superimposed
load.
Concrete
columns,
especially
those
subjected
to
bending
stresses, must always be reinforced with steel.
A
PIER
or
PEDESTAL
is
a
compressive
member
that is short (usually
the
height is less than three
times the least lateral dimension) in relation
to its
cross

sectional
area
and
carries
no
bending
stress.
In concrete
columns, vertical reinforcement is
the
principal
reinforcement.
However,
a
loaded
column shortens vertica
lly and expands
laterally;
hence, lateral reinforcements in the form of lateral
ties are used
to restrain the expansion. Columns
reinforced in this manner are called
tied columns
(fig.
7

3,
view A). If the restraining reinforcement
is a
continuous winding spiral that encircles the
core and longitudinal steel,
the column is called
a
spiral
column
(fig,
7

3,
view
B).
BEAM
AND
BEAM
REINFORCE

MENT.
—
Beams are the principal load

carrying
horizontal members. They take the load directly
from
the
floor
and
carry
it
to
the
columns.
Concrete
beams
can
either
be
cast
in
place
or
precast and transported to
the jobsite.
Figure 7

4
shows several
common types of beam reinforcing
steel shapes. Both straight and bent

up principal
Q.7
Compare prestressed concrete beam and reinforced concrete
beam.
Prestressed concrete
is a method for overcoming
concrete
's natural weakness in
tension
. It can be u
sed to
produce
beams
,
floors
or
bridges
with a longe
r
span
than is practical with ordinary
reinforced concrete
. Prestressing
tendons
(generally of high
tensile
steel
cable
or
rods
) are used to provide a clamping load which produces
a
compressive stress
that balances the
tensile stress
that the concrete
compression member
would otherwise
experience due to a bending load. Tradition
al
reinforced concrete
is based on the use of
steel
reinforcement
bars,
rebars
, inside poured
concrete
.
Prestressing can be accomplished in three ways: pre

tensioned concrete, and bonded or unbonded post

tensioned
concrete.
Pre

tensione
d concrete is cast around already tensioned tendons. This method produces a good bond
between the tendon and concrete, which both protects the tendon from corrosion and allows for
direct transfer of tension. The cured concrete adheres and bonds to the bars
and when the
tension is released it is transferred to the concrete as compression by static
friction
. However, it
requires stout anchoring points between which the tendon is to be stretched
and the tendons are
usually in a straight line. Thus, most pretensioned concrete elements are
prefabricated
in a
factory and must be transported to the construction site, which
limits their size. Pre

tensioned
elements may be
balcony
elements,
lintels
, floor slabs, beams or foundation
piles
. An
innovative
bridge
construction method using pre

stressing is the
stressed ribbon bridge
design.
Reinforced concrete
is
concrete
in which reinforcement bars ("
r
ebars
"), reinforcement grids,
plates
or
fibers
have
bee
n incorporated to strengthen the concrete in
tension
. It was invented by
French
gardener
Joseph Monier
in 1849
and
patented
in 1867.
[1]
The term Fer
ro Concrete refers only to concrete that is reinforced with iron or steel. Other
materials used to reinforce concrete can be organic and inorganic fibres as well as
comp
osites
in different forms.
Prior to the invention of reinforcement, concrete was strong in
compression
, but weak in tension. Adding
reinforcement crucially increases the strength in tension. The failure strain of concrete in tension is so low that the
reinforcement has to hold the cracked sections together.
For a strong, ductile and durable construction th
e reinforcement needs to have the following properties:
High strength
High tensile strain
Good bond to the concrete
Thermal compatibility
Durability in the concrete environment
In most cases reinforced concrete uses steel rebars that have been inserted to
add strength.
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