DESIGN METHODS OF RCC, DESIGN PHILOSOPHY OF LSM

1. DESIGN OF RC ELEMENTS
K.S.PRASATH
Assistant Professor
Department of Civil Engineering
Sri Manakula Vinayagar Engineering College
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2. UNIT I
METHODS OF DESIGN OF
CONCRETE STRUCTURES
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3. MATERIALS - CEMENT
Types of cement IS No Purpose
OPC 269-1976 General construction
Low heat cement 269-1976 Massive construction
Rapid hardening
cement
8041-1990 For quick removal of
formwork
Pozzolona cement 1489-1991 Chemical resistance
High strength cement 8112-1989 Prestressed concrete
Hydrophobic cement 8043-1991 Water proof
construction
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4. GRADES OF CEMENT
• Grades of cement is based on crushing strength of a cement mortar
cube of size 70.71 mm (surface area of 50 cm2)cured and tested at
28 days. They basically differ in terms of fineness of cement which
in turn is expressed as specific surface area
• Specific surface area is the surface area of the particles in 1 gram of
cement (unit: cm2 /gram). Chemically all the three grades of
cement viz. grade 33, grade 43 and grade 53 are almost similar (IS
516 – 1959)
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5. Conti..
• Their characteristics are listed below
– Grade 33 – specific surface area is minimum 2250 cm2 /gram
(IS:269)
– Grade 43 – specific surface area is minimum 3400 cm2 /gram
(IS:8112-1969)
– Grade 53 – specific surface area is minimum 3400 cm2 /gram
(IS:12269-1987)
• Grade 53 cements have more shrinkage compared to other grades, but
having higher early strength. Therefore preferred for high strength
concretes, prestressed concretes etc.
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6. AGGREGATES
• As per IS 383-1970 – Generally Hard Blasted Granite Chips (HBG)
COARSE AGGREGATE
• Nominal maximum size of coarse aggregate for RCC is 20 mm
• In no case greater than one fourth of minimum thickness of
member
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7. Conti..
• In heavily reinforced members 5 mm less than the minimum clear
distance between the main bars or 5 mm less than the minimum
cover to the reinforcement which ever is smaller
FINE AGGREGATE
• Generally medium sand, Zone II sand as per IS 456
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8. REINFORCEMENT
• Mild steel and medium tensile steel bars – IS 432
• Hot rolled deformed bars – IS 1139
• Cold twisted bars – IS 1786
• Hard drawn steel wire fabric – IS 1566
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15. Reinforced Concrete
• Reinforced concrete is a building material in which two or more
materials with different physical properties are used to impart a
higher tensile strength and ductility to a building's structure.
• If concrete is not reinforced, then it tends to have low tensile
strength and ductility
• The purpose of reinforcement is to mitigate the tensile stresses that
a building structure faces on a regular basis due to natural weather
conditions.
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16. Conti..
• The reinforcement of concrete is often accomplished with the use of
steel reinforcement bars or rebars, but it can also be done by using
additional concrete passively.
• The reinforcement materials usually consist of steel, composites or
polymers, which impart strength, ductility and reinforcement to a
concrete structure.
Reinforced concrete can be classified as:
– Precast concrete
– Cast in place concrete 16

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18. 18

19. CONCRETE
CHARACTERISTICS STRENGTH
• The strength of material below which not more than 5 % of test
results are expected to fall
• The compressive strength of 15 cm cube cured for 28 days,
expressed in N/mm2
• Individual variation in the compressive strength of three cubes in
the sample should not exceed ±15%
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20. Conti..
MINIMUM GRADES OF CONCRETE FOR VARIOUS STRUCTURES
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Types of construction Minimum grade of concrete
Lean concrete bases M5 and M7.5
Plain cement concrete (PCC) M10
RCC (General Construction) M20
Water tanks, domes, folded plates,
shell roofs
M20
RCC in sea water(General
Construction
M30 for RCC & M20 for PCC
Post tensioned Pre- stressed
concrete
M30
Pre tensioned Pre- stressed concrete M30

21. Conti..
TYPES OF CONCRETE AS PER IS 456-2000
• Ordinary Concrete = M10 to M20
• Standard Concrete = M25 to M55
• High Strength Concrete = M60 to M80
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22. Conti..
PROPERTIES OF CONCRETE
• Increase in strength with age (Age factors)
– 1 month – 1.0, 3 month – 1.1, 6 month – 1.15, 12 month – 1.2
• Tensile strength of concrete (fcr): test conducts are
– Flexural (modulus of rupture) test &
– Split tensile strength test
– Empirical formula given by IS 456-200 is fcr= 0.7 √fck N/mm2,
• Modulus of elasticity of concrete:
– short term modulus of elasticity Es = 5000 √fck N/mm2,
– Long term modulus of elasticity Ece =
𝑬𝒄
𝟏+θ

23. Conti..
PROPERTIES OF CONCRETE
• Creep coefficient (θ): ultimate creep strain/ Elastic strain at age of
loading
– θ values at 7 days – 2.2, 28 days – 1.6, 1 year – 1.1
• Approximate value of shrinkage strain of concrete = 0.0003
• Workability of concrete: slump test(field test) and the other tests
are compacting factor test and Vee Bee consistometer test.
• Durability: The property by which concrete possesses same strength
through out its life time. Without much of shrinkage and cracking

24. Conti..
PROPERTIES OF CONCRETE
• Factors effecting durability are w/c and maximum cement
content
• Maximum cement content as per IS 456-2000 is (without fly
ash and slag) = 450 kg/m3,
• Minimum cement content is based on exposure conditions

25. Conti..

26. Conti..
PROPORTIONS FOR CONCRETE MIXES
• Nominal Concrete Mixes: M5, M7.5, M10, M15, M20
• Design mixes for higher grades, M15 – 1:2:4, M20 – 1:1.5:3
• Quantity of water required per one bag of cement for M15 mix
is 32 liters, for M20 mix is 30 liters
• Weight batching is preferred compared to nominal(volume)
batching

27. Conti..
OPTIONAL TEST REQUIREMENTS OF CONCRETE
• After 7 days the strength should be at least two thirds of 28 days
cube strength
FACTORS AFFECTING CRUSHING STRENGTHS OF CUBES
• Size factor: As the size of the cube decreases strength increases
because of better homogeneity. For example, cube of 100 mm size
will have 5 % more strength than 150 mm cube
• Shape factor: standard cylinder of 150 mm diameter and 300 mm
height will have strength of 80 % of that of a standard cube of 150
mm

28. Conti..
FACTORS AFFECTING CRUSHING STRENGTHS OF CUBES
• Slenderness ratio : As slenderness ratio of a specimen increases,
strength decreases.
• For example: if compressive strength of a standard cylinder of
150mm diameter and 300 mm height (slenderness ratio 2) is 0.8fck,
the strength with slenderness ratio 3 is about 0.7 to 0.75fck and
with slenderness ratio 4 is about 0.67 fck

29. Conti..
FACTORS AFFECTING CRUSHING STRENGTHS OF CUBES
• Further it is observed that with increased slenderness ratio beyond
4, the strength is about 0.67 fck only. This is one of the main reason
why strength of concrete is considered as 0.67 fck instead of fck in
limit state method
EXPANSION JOINTS
• Structures more than 45 m length should be designed with one or
more expansion joints

30. DIFFERENT METHODS OF DESIGN
OF CONCRETE
1. Working Stress Method
2. Ultimate Load Method
3. Limit State Method
4. Probabilistic Method of Design
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33. 33

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43. 43

44. WORKING STRESS METHOD
• This was the traditional method of design not only for reinforced
concrete, but also for structural steel and timber design.
• The method basically assumes that the structural material behaves
as a linear elastic manner, and that adequate safety can be ensured
by suitably restricting the stresses in the material induced by the
expected “working loads” on the structure.
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45. WORKING STRESS METHOD
• As the specified permissible stresses are kept well below the
material strength, the assumption of linear elastic behavior is
considered justifiable.
• The ratio of the strength of the material to the permissible stress is
often referred to as the factor of safety.
• However, the main assumption linear elastic behavior and the tacit
assumption that the stresses under working loads can be kept
within the ‘permissible stresses’ are not found to be realistic.
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46. WORKING STRESS METHOD
• Many factors are responsible for this such as a long term effort of
creep and shrinkage, the effects of stress concentrations, and other
secondary effects.
• All such effects resulting significant local increases in a
redistribution of the calculated stresses.
• The design usually results in relatively large sections of structural
members, thereby resulting in better serviceability performance
under the usual working loads.
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47. ULTIMATE LOAD METHOD
• With the growing realization of the shortcomings of WSM in
reinforced concrete design, and with increased understanding of
the behavior of reinforced concrete at ultimate loads, the ultimate
load of design is evolved and became an alternative to WSM.
• This method is sometimes also referred to as the load factor
methods are the ultimate strength.
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48. ULTIMATE LOAD METHOD
• In this method, the stress condition at the site of impending collapse of
the structure is analyzed, and the nonlinear stress-strain curves of
concrete and steel are made use of.
• The concept of ‘modular ratio’ and its associated problems are avoided
entirely in this method.
• The safety measure design is introduced by an appropriate choice of the
load factor, defined as the ratio of the ultimate load to the working load.
• The ultimate load method makes it possible for different types of loads to
be assigned different load factors under combined loading conditions,
thereby overcoming the related shortcoming of WSM. 48

49. ULTIMATE LOAD METHOD
• This method generally results in more slender sections, and often
economical designs of beams and columns, particularly when high
strength reinforcing steel and concrete are used.
• However, the satisfactory ‘strength’ performance at ultimate loads
does not guarantee satisfactory ‘serviceability’ performance at the
normal service loads.
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50. ULTIMATE LOAD METHOD
• The designs sometimes result in excessive deflections and crack-
widths under service loads, owing to the slender sections resulting
from the use of high strength reinforcing steel and concrete.
• The distribution of stress resultants at ultimate load is taken as the
distribution at the service loads, magnified by the load factor(s); in
other words, analysis is still based on linear elastic theory.
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51. LIMIT STATE METHOD
• The philosophy of the limit state method of design represents a definite
advancement over the traditional design philosophies.
• Unlike WSM which based calculations on service load conditions alone,
and unlike ULM, which based calculations on ultimate load conditions
alone, LSM aims for a comprehensive and rational solution to the design
problem, by considering safety at ultimate loads and serviceability at
working loads.
• The LSM philosophy uses a multiple safety factor format which attempts
to provide adequate safety at ultimate loads as well as adequate
serviceability at service loads, by considering all possible ‘Limit State’.51

52. LIMIT STATE METHOD
• A limit state is a state of impending failure, beyond which a structure
ceases to perform its intended function satisfactorily, in terms of either
safety of serviceability i.e. it either collapses or becomes
unserviceable.
• There are two types of limit states: Ultimate limit states (limit states of
collapse):- which deal with strength, overturning, sliding, buckling,
fatigue fracture etc. Serviceability limit states: - which deals with
discomfort to occupancy and/ or malfunction, caused by excessive
deflection, crack width, vibration leakage etc., and also loss of
durability etc. 52

53. PRINCIPLE LIMIT STATES
The important states are
• The limit state of collapse in
– Flexure (Bending)
– Compression
– Shear
– Torsion
• The limit state of serviceability
– Deflection
– Cracking
– vibration 53

54. PHILOSOPHY
• Limit state design is a method of designing structures based on a
statistical concept of safety and the associated statistical probability
of failure. The method of design for a structure must ensure an
acceptable probability that the structure during its life will not
become unfit for its intended use
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55. DESIGN LOADS
• The design loads for various limit states are obtained as the product
of the characteristics loads and partial safety factors and are
expressed as
• Fd = F. γf
– Where, F = characteristics load
– γf = Partial safety factor appropriate to the nature of loading and
the limit state
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56. Conti..
Characteristic load
• The load which has 95% probability of not being exceeding in the
life time of a structure
Values of partial safety factor “γf” for loads
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57. NOTE
• While considering earthquake effects, substitute EL for WL
• For the limit states of serviceability, the values of γf given in this
table are applicable for short term effects. While assessing the long
term effects due to creep the dead load and that part of the live
load likely to be permanent may only be considered
• The values is to be considered when stability against overturning or
stress reversal is critical 57

58. DESIGN STRENGTH
• The design strength of the material “Fd ” is given by
• Fd = f/γm
– Where, f = characteristic strength of the material
– γm = Partial safety factor appropriate to the material and the limit state being
considered.
– Values of partial safety factor “γm ” for material strength
Limit state of collapse, ϒm
• Steel – 1.15, Concrete – 1.5
Limit state of serviceability
• Steel – 1.00, Concrete – 1.00 58

59. ASSUMPTIONS
• Plane sections normal to the axis of the member remain plane after
bending
• The tensile strength of concrete is ignored
• The maximum strain in concrete at the outermost compression fibre
is 0.0035
• The compressive stress strain curve may be assumed to be
rectangular, trapezoidal, parabola or any other shape which results
in the prediction of strength in substantial agreements with the
results of tests.
– An acceptable stress strain curve( rectangular-parabolic) is shown aside 59

60. Conti..
– Compressive strength of concrete in the structure is assumed to be
0.67 times the characteristics strength of the concrete
– The partial strength of concrete in addition to it
– Therefore, the design strength of concrete is 0.67fck/1.5 i.e. 0.446fck
or 0.45 fck
– The design stress in reinforcement is derived from the stress strain
curves given below for mild steel and cold work deformed bars
respectively. The partial factor of safety “γm ” equal to 1.15 is
applied to the strength of reinforcement. Therefore the design
strength of reinforcement is fy /1.5 i.e. fy
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61. CONCRETE
61
COLD DEFORMED BAR

62. STEEL BAR WITH DEFINITE YIELD POINT
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63. Conti..
• The maximum strain in the tension reinforcement in the
section at failure should not be less than
0.002+
𝟎.𝟖𝟕𝒇𝒚
𝑬𝒔
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64. LIMIT STATE METHOD OF
DESIGN
• The object of the design based on the limit state concept is to
achieve an acceptable probability, that a structure will not become
unsuitable in it’s lifetime for the use for which it is intended, i.e. It
will not reach a limit state
• A structure with appropriate degree of reliability should be able to
withstand safely.
• All loads, that are reliable to act on it throughout it’s life and it
should also satisfy the subs ability requirements, such as limitations
on deflection and cracking. 64

65. SINGLY REINFORCED BEAM
• In singly reinforced simply supported beams or slabs reinforcing
steel bars are placed near the bottom of the beam or slabs where
they are most effective in resisting the tensile stresses.
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66. Reinforcement in simply
supported beam
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67. Reinforcement in a cantilever
beam
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68. CONCRETE
68
COLD DEFORMED BAR
Stress Strain curve

69. STRESS BLOCK PARAMETERS
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70. OVER ALL DEPTH
• The normal distance from the top edge of the beam to the bottom
edge of the beam is called over all depth. It is denoted by ‘D’.
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EFFECTIVE DEPTH
• The normal distance from the top edge of beam to the center of
tensile reinforcement is called effective depth. It is denoted by ‘d’.

71. CLEAR COVER
• The distance between the bottom of the bars and bottom most the
edge of the beam is called clear cover. CLEAR COVER = 25mm or dia
of main bar, (Which ever is greater).
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EFFECTIVE COVER
• The distance between center of tensile reinforcement and the
bottom edge of the beam is called effective cover. Effective cover =
clear cover + ½ dia of bar.

72. END COVER
• END COVER = 2*DIA OF BAR OR 25mm (WHICH EVER IS GREATER)
72
NEUTRAL AXIS
• The layer / lamina where no stress exist is known as neutral axis. It
divides the beam section into two zones, compression zone above
the neutral axis & tension zone below the neutral axis.

73. Conti..
• Depth of neutral axis:- the normal distance between the top edge of
the beam & neutral axis is called depth of neutral axis. IT IS
DENOTED BY ‘n’.
• Lever arm:- the distance between the resultant compressive force
(c) and tensile force (t) is known as lever arm. IT IS DENOTED BY ‘z’.
The total compressive force (c) in concrete act at the C.G OF
COMPRESSIVE STRESS DIAGRAM i.e. n/3 from the compression
edge. The total tensile force (t) acts at C.G of the reinforcement.
LEVER ARM = d-n/3
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74. Conti..
• Tensile reinforcement:- the reinforcement provided tensile zone is
called tensile reinforcement. It is denoted by Ast.
• Compression reinforcement :- the reinforcement provided
Compression zone is called compression reinforcement. It is
denoted by Asc
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75. Conti..
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76. TYPES OF BEAM SECTION
BALANCED SECTION
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A section is Known as balanced section in which The compressive
stress in concrete (in Compressive zones) and tensile stress In
steel will both reach the maximum Permissible values
simultaneously. The neutral axis of balanced (or Critical) section
is known as critical NEUTRAL AXIS (Xumax). The area of steel
Provided as economical area of steel. Reinforced concrete
sections are Designed as balanced sections.

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78. UNDER REINFORCED SECTION
78
If the area of steel provided is less than that required for
balanced section, it is known as under reinforced section. due to
less reinforcement the position of actual neutral axis (Xu) will shift
above the critical neutral axis (Xumax) i.e. Xu< Xumax . in under-
reinforced section steel is fully stressed and concrete is under
stressed (i.e. Some concrete remains un-utilised). Steel being
ductile, takes some time to break. This gives sufficient warning
before the final collapse of the structure. For this reason and
from economy point of view the under-reinforced sections are
designed.

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80. OVER REINFORCED SECTION
80
If the area of steel provided is more than that required for a
balanced section, it is known as over-reinforced section. As the
area of steel provided is more, the position of N.A. will shift
towards steel, therefore actual axis (Xu) is below the critical
neutral axis (Xumax) i.e. Xu> Xumax . In this section concrete is fully
stressed and steel is under stressed. Under such conditions, the
beam will fail initially due to over stress in the concrete. Concrete
being brittle, this happens suddenly and explosively without any
warning.

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