2. Topics Covered in this unit are
Description of topic No. of Hrs.
Introduction to RCC 1
Constituents of concrete , grades of concrete 2
Recommendations of I.S. 456 – 2000 1
Assumptions in elastic theory &Derivation
of Stress block parameters
1
Problems on finding Moment of
resistance, stresses in concrete and steel
and design of singly reinforced
Rectangular beams
2
Tutorial on singly reinforced beams 1
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3. LEARNING OBJECTIVES
After completion of this unit, student will be able
to
• Identify the various materials used in concrete
• List the various grades of concrete
• Acquaintance with the Codal provisions of IS
456 – 2000
• List the salient features of elastic theory and
assumptions in it
• Design a Singly reinforced Rectangular Section
using working stress method
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9. • Concrete is everywhere!!
Roads, sidewalks, houses, bridges,
skyscrapers, pipes, dams, canals, missile
silos, and nuclear waste containment
The word concrete comes from the Latin word
"concretus" (meaning compact or condensed),
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12. • When was concrete first made?
500 BC
• What is the purpose of cement in concrete?
It acts as a primary binder to join the aggregate
into a solid mass.
• What role does water play in producing concrete?
Water is required for the cement to hydrate and
solidify.
• Why does concrete harden?
The chemical process called cement hydration
produces crystals that interlock and bind together.
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13. • Why does concrete set (harden) slowly?
It takes time for the hydrated cement
crystals to form
• Is concrete stronger in compression,
tension, or the same in either?
It is stronger in compression.
• How long can concrete last (in years)?
50,000
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14. • Concrete is strong in Compression but
weak in tension, thus adding
reinforcement increases the strength in
tension
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15. • Concrete is reinforced to give it extra
tensile strength; without reinforcement,
many concrete buildings would not have
been possible.
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16. Concrete Reinforcing
• Concrete - No Useful Tensile Strength
• Reinforcing Steel - Tensile Strength
– Similar Coefficient of thermal expansion
– Chemical Compatibility
– Adhesion Of Concrete To Steel
• Theory of Steel Location
“Place reinforcing steel where the
concrete is in tension”
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17. • Reinforced concrete can encompass many
types of structures and components,
including
slabs,beams,columns,foundations,frames
and more.
• Reinforced concrete can be classified as
precast or cast-in-situ
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18. Concrete Properties
• Versatile
• Pliable when mixed
• Strong & Durable
• Does not Rust or Rot
• Does Not Need a Coating
• Resists Fire
• It can be molded to just about any
shape.
21. flower pots &
planters
chimneys mantels
ballast bath tubs grave vaults
bank vaults basements lamp posts
telephone poles
electric light
poles
Frisbees
headstones steps fence posts
business/credit
cards **
fertilizer bone replacement **
insulating tiles/bricks corn silos park benches
parking stones roof tiles water troughs
water tanks curb & gutters
nuclear reactor containment
structures
artificial rocks office buildings parking lots
railroad ties airports monorails
picnic tables swimming pools break waters
wharves & piers bird baths barbecue pits
stadium seats fountains lunar bases **
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22. Concrete
• Rocklike Material
• Ingredients
– Portland Cement
– Course Aggregate
– Fine Aggregate
– Water
– Admixtures (optional)
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23. CONSTITUENT MATERIALS AND PROPERTIES (
Types of cement (CSA)
- Standard Portland cement - Used for general purposes; air entrained
(50% C3S; 24% C2S; 11%C3A; 8% C4AF; 72% passing 45 μm
sieve)
- Modified Portland cement - Used when sulphate resistance and/or
generation of moderate heat of hydration are required; air
entrained (42%
C3S; 33% C2S; 5% C3A; 13% C4AF; 72% passing 45 μm sieve)
- High early strength Portland cement - Used for early strength and
cold weather operations; air entrained (60% C3S; 13% C2S; 9% C3A;
8% C4AF; ….)
- Low heat Portland cement - Used where low heat of hydration is
required; air entrained (26% C3S; 50% C2S; 5% C3A;
12% C4AF; …….)
- High sulphate-resistant concrete - Used where sulphate
concentration is very high; also used for marine and sewer
structures; air entrained (40% C3S; 40 % C2S; 3.5 % C3A; 9%
C4AF; 72% passing 45 μm sieve)
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24. Constituents of cement: 75% is composed of
calcium silicates; rest is made up of Al2O3, Fe2O3
and CaSO4
Di-calcium silicate (C2S) - 2CaO.SiO2 (15-40%)
Tri-calcium silicate (C3S) - 3CaO.SiO2 (35-65%)
Tri-calcium aluminate (C3A) - 3CaO.Al2O3 (0-15%)
Tetra-calcium alumino-ferrite (C4AF) -
4CaO.Al2O3..Fe2O3 (6 -20%)
Calcium sulphate - (CaSO4) (2%)
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25. CONSTITUENT MATERIALS AND PROPERTIES
Setting, Hydration and Hardening
- When cement is mixed with sufficient water, it loses its
plasticity and slowly forms into a hard rock-type material;
this whole process is called setting.
- Initial set: Initially the paste loses its fluidity and within a few
hours a noticeable hardening occurs - Measured by Vicat’s
apparatus
- Final set: Further to building up of hydration products is the
commencement of hardening process that is responsible for
strength of concrete - Measured by Vicat’s apparatus
- Gypsum retards the setting process
- Hot water used in mixing will accelerate the setting process
- During hydration process the following actions occur:
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26. CONSTITUENT MATERIALS AND PROPERTIES
2(3CaO.SiO2) + 6H2O = 3CaO.2SiO2.3H2O + 3Ca(OH)2
(Tricalcium silicate) (Tobermerite gel)
2(2CaO.SiO2) + 4H2O = 3CaO.2SiO2.3H2O+Ca(OH)2
(Dicalcium silicate) (Tobermerite gel)
3CaO.Al2O3 + 12H2O + Ca(OH)2 = 3CaO. Al2O3. Ca(OH)2.12H2O
(Tricalcium aluminate) (Tetra-calcium aluminate hydrate)
4CaO.Al2O3..Fe2O3 + 10H2O + 2Ca(OH)2 = 6CaO. Al2O3. Fe2O3.12H2O
(Tetra-calcium alumino-ferrite) (Calcium alumino-ferrite hydrate)
3CaO.Al2O3+10H2O+ CaSO4.2H2O = 3CaO.Al2O3.CaSO4.12H2O
(Tricalcium aluminate) (Calcium sulphoaluminate hydrate)
- C3S hardens rapidly: responsible for early strength
- C2S hardens slowly and responsible for strength gain beyond one
week
- Heat of hydration: Hydration is always accompanied by release of
heat
- C3A liberates the most heat
- C2S liberates the least
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27. CONSTITUENT MATERIALS AND
PROPERTIES
Properties of Aggregates, Water and Admixtures
- Aggregates make up up 59-75% of concrete
volume; paste constitutes 25-40% of concrete
volume. Volume of cement occupies 25-45% of
the paste and water makes up to 55-75%. It also
contains air, which varies from 2-8% by volume
- Strength of concrete is dependent on the
strength of aggregate particles and the strength
of hardened paste
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28. Properties of Aggregates
compressive strength: Should be higher than concrete
strength of 40-120 MPa
Voids: Represent the amount of air space between the
aggregate particles - Course aggregates contain 30-
50% of voids and fine aggregate 35-40%
Moisture content represents the amount of water in
aggregates: absorbed and surface moisture - Course
aggregates contain very little absorbed water while
fine aggregates contain 3-5% of absorbed water and
4-5% surface moisture
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29. Properties of Water
Any drinkable water can be used for concrete
making - Water containing more than 2000 ppm of
dissolved salts should be tested for its effect on
concrete
- Chloride ions not more than 1000 ppm - Sulphate ions
not more than 3000 ppm
- Bicarbonate ions not more than 400 ppm
• The water should satisfy the requirements of Section 5.4
of IS:456 - 2000.
• “Water used for mixing and curing shall be clean and
free from injurious amounts of oils, acids, alkalis, salts,
sugar, organic materials or other substances that may be
deleterious to concrete and steel”.
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30. Admixtures
Admixture are materials that are added to plastic
concrete to change one or more properties of
fresh or hardened concrete.
To fresh concrete: Added to influence its
workability, setting times and heat of hydration
To hardened concrete : Added to
influence the concrete’s durability and strength
Types: Chemical admixtures and mineral
admixtures
Chemical: Accelerators, retarders, water-
reducing and air-entraining
Mineral : Strength and durability
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31. • The common chemical admixtures
are as follows.
–1) Air-entraining admixtures
–2) Water reducing admixtures
–3) Set retarding admixtures
–4) Set accelerating admixtures
–5) Water reducing and set retarding
admixtures
–6) Water reducing and set accelerating
admixtures.
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32. • The common mineral admixtures are as
follows.
– 1) Fly ash
– 2) Ground granulated blast-furnace slag
– 3) Silica fumes
– 4) Rice husk ash
– 5) Metakoline
• These are cementitious and pozzolanic
materials.
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33. Fly ash: By-product of coal from electrical
power plants - Finer than cement -
Consists of complex compounds of silica,
ferric oxide and alumina - Increases the
strength of concrete and decreases the
heat of hydration - Reduces alkali
aggregate reaction.
Silica fume: By-product of electric arc
furnaces - Size less than 0.1μm - Consists
of non-crystalline silica - Increases the
compressive strength by 40-60%
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34. Properties of Hardened Concrete
The concrete in prestressed applications has to be of good quality. It
requires the following attributes.
1) High strength with low water-to-cement ratio
2) Durability with low permeability, minimum cement
content and proper mixing, compaction and curing
3) Minimum shrinkage and creep by limiting the cement
content.
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35. 1) Strength of concrete
2) Stiffness of concrete
3) Durability of concrete
4) High performance concrete
5) Allowable stresses in concrete.
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36. Strength of Concrete
The following sections describe the properties with
reference to IS:1343 - 1980. The strength of concrete is
required to calculate the strength of the members. For
prestressed concrete applications, high strength
concrete is required for the following reasons.
– 1) To sustain the high stresses at anchorage regions.
– 2) To have higher resistance in compression, tension, shear
and bond.
– 3) To have higher stiffness for reduced deflection.
– 4) To have reduced shrinkage cracks
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37. Compressive Strength
The compressive strength of concrete is given in
terms of the characteristic compressive
strength of 150 mm size cubes tested at 28
days (fck). The characteristic strength is
defined as the strength of the concrete
below which not more than 5% of the test
results are expected to fall. This concept
assumes a normal distribution of the strengths of
the samples of concrete.
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38. • Idealized distribution of the values of
compressive strength for a sizeable
number of test cubes
• The horizontal axis represents the values
of compressive strength. The vertical axis
represents the number of test samples for
a particular compressive strength.
(frequency)
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40. • The average of the values of compressive
strength (mean strength) is represented as
f cm.
• The characteristic strength (fck) is the
value in the x-axis below which 5% of the
total area under the curve falls.
• The value of fck is lower than fcm by 1.65σ,
where σ is the standard deviation of the
normal distribution.
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41. What is grade of concrete?
• Grade of concrete refers to the strength of
concrete after a period of 28 days, i.e. M20
grade refers to strength of concrete after 28
days as 200kg / cm square or
20 N/mm2 or 20 MPa
Concrete cubes measuring 150mm x 150mm x
150mm are cast at regular intervals and the
same cubes are tested to find out crushing
strength on 7th and 28th day. The strength of the
cube, which is the representative sample of the
concrete, will indicate strength of concrete,
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42. • M 20 refers to grade of concrete wherein
M refers to mix viz aggregate,
sand,cement..and
• 20 refers to the "characteristic"
compressive strength in N/mm2 of a 15
cm cube casted out of that concrete...
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43. GRADES OF CONCRETE
• The grades of concrete are explained in Table 1 of
the Code.
• The minimum grades of concrete for prestressed
applications are as follows.
• 30 MPa for post-tensioned members
• 40 MPa for pre-tensioned members.
• The maximum grade of concrete is ? MPa.
• The increase in strength with age as given in IS:1343
- 1980, is not observed in present day concrete that
gains substantial strength in 28 days. Hence, the age
factor given in Clause 5.2.1 should not be used. It
has been removed from IS:456 - 2000.
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44. Design of concrete Mix
• Nominal mix concrete
• Design mix concrete
• The proportions of cement,sand,coarse
aggregate for a design strength can be
adopted or rationally designed
45. Nominal mix
• A concrete mix in which the proportions
are adopted by volume is referred to as
Nominal mix
Design Mix
• A concrete mix in which the proportions
are adopted to achieve desired strength is
referred to as Design mix
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46. Tensile Strength
• The tensile strength of concrete can be
expressed as follows.
1) Flexural tensile strength: It is measured by
testing beams under 2 point loading (also called 4
point loading including the reactions).
2) Splitting tensile strength: It is measured by
testing cylinders under diametral compression
3) Direct tensile strength: It is measured by testing
rectangular specimens under direct tension.
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47. • In absence of test results, the Code
recommends to use an estimate of the
flexural tensile strength from the
compressive strength by the following
equation.
• fcr = flexural tensile strength in N/mm2
• fck = characteristic compressive strength of
cubes in N/mm2.
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48. Stiffness of Concrete
• The stiffness of concrete is required to
estimate the deflection of members. The
stiffness is given by the modulus of
elasticity.
• For a non-linear stress (fc) versus strain (εc)
behaviour of concrete the modulus can be
initial, tangential or secant modulus.
• The modulus of elasticity for short term
loading (neglecting the effect of creep) is
given by the following equation.
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49. Durability of Concrete
• The durability of concrete is of vital
importance regarding the life cycle cost of
a structure. The life cycle cost includes not
only the initial cost of the materials and
labour, but also the cost of maintenance
and repair.
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50. high performance concrete
• Some special types of high performance
concrete are as follows.
1) High strength concrete
– 2) High workability concrete
– 3) Self-compacting concrete
– 4) Reactive powder concrete
– 5) High volume fly ash concrete
– 6) Fibre reinforced concrete
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51. DESIGN PHILOSOPHIES
• THE WORKING STRESS METHOD
• THE ULTIMATE LOAD METHOD or LOAD
FACTOR METHOD
• THE LIMIT STATE METHOD
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53. • The method is designated as working
stress method as the loads for the design
of structures are the service loads or the
working loads. The failure of the structure
will occur at a much higher load. The ratio
of the failure loads to the working loads is
the factor of safety.
54. Assumptions in working stress
method
• A section which is plane before remain
plane after bending.
• Bond between steel and concrete is
perfect within elastic limit of steel
• The tensile strength of concrete is ignored
• Concrete is elastic,i.e the stress in
concrete varies linearly from zero at the
neutral axis to a minimum at the extreme
fibre
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55. • The modular ratio,m has the
value(280/3σcbc) where σcbc is the
permissible compressive stress in bending
In N/mm2 or MPa
Permissible stresses are prescribed by building code
to provide suitable factors of safety to allow for
uncertainities in estimation of working loads and
variation in properties of materials.
FS=3 for concrete
=1.78 for steel as per IS:456
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56. • Working stress can be expressed as
μ R >L
μ =inverse of factor of safety which is less
than unity
R= resistance of the structural elements
L= working loads on the structural elements
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57. Drawbacks of working stress method
• Concrete is not elastic. The inelastic behaviour of
concrete starts right from very low stresses. The
actual stress distribution in a concrete section
cannot be described by a triangular stress diagram.
• Since factor of safety is on the stresses under
working loads, there is no way to account for
different degrees of uncertainty associated with
different types of loads. With elastic theory it is
impossible to determine the actual factor of safety
with respect to loads.
• It is difficult to account for shrinkage and creep
effects by using the working stress method.
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60. • Reinforced concrete analysis is performed
at a given section for either axial force and
bending moment or transverse shear
loads. The axial force and bending
moment analysis usually idealizes the
stress-strain behavior of the concrete with
a rectangular stress block to simplify the
calculations
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62. • x = kd = depth of the neutral axis, where k is a factor,
– fcbc = actual stress of concrete in bending compression at
the top fibre which should not exceed the respective
permissible stress of concrete in bending compression
σcbc,
– fst = actual stress of steel at the level of centroid of steel
which should not exceed the respective permissible stress
of steel in tension σst,
– jd = d(1-k/3) = lever arm i.e., the distance between lines of
action of total compressive and tensile forces C and T ,
respectively.
• the value of the stress at the level of centroid of steel of
Fig. is fst /m due to the transformation of steel into
equivalent concrete of area mAst.
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63. Types of Problems
• Analysis of a section
• Design of a section
Types of sections
Under reinforced section
Balanced section
Over reinforced section
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64. • Analysis Type of Problems
For the purpose of analysing a singly-reinforced
beam where the working loads, area of steel, b and d
of the cross section are given, the actual stresses of
concrete at the top fibre and steel at the centroid of
steel are to be determined in the following manner.
Step 1: To determine the depth of the neutral axis kd
from Eq. 13.16.
Step 2: The beam is under-reinforced, balanced or over-
reinforced, if k is less than, equal to or greater than
kb, to be obtained from Eq. 13.3.
Step 3: The actual compressive stress of concrete fcbc
and tensile stress of steel at the centroid of steel fst
are determined in the following manner for the three
cases of Step 2.
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65. Case (i) When k < kb (under-reinforced section)
From the moment equation, we have
M= Ast fst d(1 - k/3)
or fst =M /{Ast d(1 - k/3)} (13.24)
where M is obtained from the given load, Ast and d are given, and
k is determined in Step 1.
Equating C = T, we have: (1/2) fcbc b(kd) = Ast fst
or fcbc = (2 Ast fst) / (b kd) (13.25)
where Ast, b and d are given and k and fst are determined in steps
1 and 2, respectively.
Case (ii) When k = kb (balanced section)
In the balanced section fcbc = σcbc and fst = σst.
Case (iii) When k > kb (over-reinforced section)
Such beams are not to be used as in this case fcbc shall reach
σcbc while fst shall not reach σst. These sections are to be
redesigned either by increasing the depth of the beam or by
providing compression reinforcement. Beams with
compression and tension reinforcement are known as doubly
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66. Step 1. Selection of preliminary
dimension b and D
Step 2. Determination of d
Step 3. Determination of Ast
Step 4. Checking for the stresses
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67. • The working stress model assumes a
constant increase in compression strain
form the neutral axis to the outer
compression fiber and no concrete
tension.
• Only the rebar contributes to the moment
tension. This is because the concrete is
assumed to be fully cracked by the tensile
stress
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68. Assignment-1
• What is grading of concrete & grading of aggregate?
Explain in detail the role of grading on properties of
concrete.
• Explain environmental exposure conditions as given
in IS:456-2000.
• Explain under reinforced, over reinforced & balanced
sections.
• Explain durability requirements as per IS:456-2000.
• Explain how concrete is divided into different grades
based on strength as per IS:456-2000.
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