Plain and Reinforced Concrete
Concrete
 Concrete is a mixture of cement, fine and coarse aggregate.
 Concrete mainly consists of a binding material and filler material. If filler material size is < 5mm it is fine aggregate and > 5mm is coarse aggregate.
Plain Cement Concrete (PCC)
 Mixture of cement , sand and coarse aggregate without any reinforcement is known as PCC.

PCC is strong in compression and week in tension. Its tensile strength is so small that it can be neglected in design.
Reinforced Cement Concrete (RCC)
 Mixture of cement , sand and coarse aggregate with reinforcement is known as RCC. (Tensile strength is improved)
 Mix Proportion
Cement  :  Sand  :  Crush 
1  :  1.5  :  3 
1  :  2  :  4 
1  :  4  :  8 
 Water Cement Ratio (W/C) W/C = 0.5 – 0.6
 For a mix proportion of 1:2:4 and W/C = 0.5, if cement is 50 kg
Sand = 2 x 50 = 100 Kg
Crush = 4 x 50 = 200 Kg Batching By Weight
Water = 50 x 0.5 = 25 Kg
Mechanism of Load Transfer
Function of structure is to transfer all the loads safely to ground. A particular structural member transfers load to other structural member.
Merits of Concrete Construction
4.Good Insulation Concrete is a good insulator of Noise & heat and does not allow them to transmit completely.
Demerits of Concrete Construction
3.Cracking Unlike steel structures concrete structures can have cracks. More cracks with smaller width are better than one crack of larger width
Specification & Codes
These are rules given by various organizations in order to guide the designers for safe and economical design of structures. Various Codes of Practices are
 ACI 31805 By American Concrete Institute. For general concrete constructions (buildings)
 AASHTO Specifications for Concrete Bridges. By American Association of State Highway and Transportation Officials.
 ASTM (American Standards for Testing and Materials) for testing of materials.
No code or design specification can be construed as substitute for sound engineering judgment in the design of concrete structures. In the structural practice, special circumstances are frequently encountered where code provisions can only serve as a guide, and engineer must rely upon a firm understanding of the basic principles of structural mechanics applied to reinforced or prestressed concrete, and the intimate knowledge of nature of materials
Design Loads
 They may be either fully or partially in place or not present at all, and may also change in location.
 Their magnitude and distribution at any given time are uncertain, and even their maximum intensities throughout the life time of the structure are not known with precision.
 The minimum live loads for which the floor and roof of a building should be designed are usually specified in the building codes that governs at the site construction.
Densities of Important Materials
Material  Density (Kg/m^{3}) 
PCC  2300 
RCC  2400 
Brick masonry  19001930 
Earth/Sand/Brick ballast  16001800 
Intensities of Live Loads
(Table 1.1, Design of concrete structures by Nilson)
Occupancy / Use  Live Load(Kg/m2) 
Residential/House/Class Room  200 
Offices  250500 
Library Reading Room  300 
Library Stack Room  750 
Warehouse/Heavy storage  1250 
Basic Design Equation
Applied Action x F.O.S = Max. Internal Resistance
Factor of Safety
F.O.S. = Max. Failure load/Max. Service LoadFollowing points are relevant to F.O.S1.It is used to cover uncertainties due to
 Applied loads
 Material strength
 Poor workmanship
 Unexpected behavior of structure
 Thermal stresses
 Fabrication
 Residual stresses
2.If F.O.S is provided then at service loads deflection and cracks are within limits. 3.It covers the natural disasters.
Ultimate Strength Design (USD)/LRFD Method
Strength design method is based on the philosophy of dividing F.O.S. in such a way that Bigger part is applied on loads and smaller part is applied on material strength. Material Strength ≥ Applied Load x F.O.S.(1) x F.O.S.(2) {1 / F.O.S.(2)} Material Strength ≥ Applied Load x F.O.S.1 F.O.S.(1) = Overload factor or Load Factor {greater than 1} 1/F.O.S.(2) = Strength Reduction factor or Resistance Factor {less than 1}
ΦSn ≥ U
Where
Sn = Nominal Strength
ΦSn = Design Strength
Φ = Strength Reduction Factor
U = Required Strength, calculated by applying load factors
For a member subjected to moment, shear and axial load:
ΦMn ≥ Mu
ΦVn ≥ Vu
ΦPn ≥ Pu
Allowable Strength Design (ASD)
In allowable strength design the whole F.O.S. is applied on material strength and service loads (unfactored) are taken as it is.
Material Strength / F.O.S. ≥ Service Loads
In both Allowable strength design and Ultimate strength design analysis carried out in elastic range
Plastic Design
In plastic design, plastic analysis is carried out in order to find the behavior of structure near collapse state. In this type of design material strength is taken from inelastic range. It is observed that whether the failure is sudden or ductile. Ductile failure is most favorable because it gives an warning before the failure of structures
Capacity Analysis
In capacity analysis size, shape, material strengths and cross sectional dimensions are known and maximum load carrying capacity of the structure is calculated. Capacity analysis is generally carried out for the existing structures.
Design of Structure
In design of structure load, span and material properties are known and cross sectional dimensions and amount of reinforcement are to be determined.
Objectives of Designer
There are two main objectives
Safety
The structure should be safe enough to carry all the applied throughout the life.
Economy
Structures should be economical. Lighter structures are more economical.
Economy α 1/self weight (More valid for Steel Structures)
In concrete Structures overall cost of construction decides the economy, not just the self weight.
Load Combinations
To combine various loads in such a way to get a critical situation.
Load Factor = Factor by which a load is to be increased x probability of occurrence
Where
D = Dead load
L = Live load on intermediate floors
Lr = Live load on roof
W = Wind Load
Strength Reduction Factor / Resistance Factor, Φ
Strength Condition  Strength Reduction Factor 
Tension controlled section (bending or flexure)  0.9 
Compression controlled section  
Columns with ties  0.65 
Column with spirals  0.7 
Shear and Torsion  0.75 
Shrinkage
“Shrinkage is reduction in volume of concrete due to loss of water”
Coefficient of shrinkage varies with time. Coefficient of shortening is:
 0.00025 at 28 days
 0.00035 at 3 months
 0.0005 at 12 months
Shrinkage = Shrinkage coefficient x Length
Excessive shrinkage can be avoided by proper curing during first 28 days because half of the total shrinkage takes place during this period
Creep
“creep is the slow deformation of material over considerable lengths of time at constant stress or load”
Creep deformations for a given concrete are practically proportional to the magnitude of the applied stress; at any given stress, high strength concrete show less creep than lower strength concrete.
Compressive strength  Specific Creep 
(MPa)  10^{6} per MPa 
21  145 
28  116 
41  80 
55  58 
How to calculate shortenings due to creep?
Consider a column of 3m which is under sustained load for several years.
Compressive strength, fc’ = 28 MPa
Sustained stress due to load = 10 MPa
Specific creep for 28 MPa fc’ = 116 x 106 per MPa
Creep Strain = 10 x 116 x 106 = 116 x 105
Shortening due to creep = 3000 x 116 x 105 = 3.48 mm
Specified Compressive Strength Concrete, fc’
“28 days cylinder strength of concrete”
 The cylinder has 150mm dia and 300mm length.
 According to ASTM standards at least two cylinders should be tested and their average is to be taken.
ACI 5.1.1: for concrete designed and constructed in accordance with ACI code, fc’ shall not be less than 17.5 Mpa (2500 psi)
BSS specifies the compressive strength in terms of cube strength.
 Standard size of cube is 6”x6”x6”
 BSS recommends testing three cubes and taking their average as the compressive strength of concrete
Cylinder Strength = (0.75 to 0.8) times Cube Strength
Relevant ASTM Standards
 “Methods of Sampling Freshly Mixed Concrete” (ASTM C 172)
 Practice for Making and Curing Concrete Test Specimens in Field” (ASTM C 31)
 “Test Methods for Compressive Strength of Cylindrical Concrete Specimen” (ASTM C 39)
Testing of Samples for Compressive Strength
Cylinders should be tested in moist condition because in dry state it gives more strength.
ACI 5.6.2.1: Samples for strength tests of each class of concrete placed each day shall be taken :
 Not less than once a day
 Not less than once for each 115m3 of concrete.
 Not less than once for each 450m2 of concrete.
Code allows the site engineer to ask for casting the test sample if he regards it necessary.
Acceptance Criteria for Concrete Quality
ACI 5.6.3.3: Strength level of an individual class of concrete shall be considered satisfactory if both of the following requirements are met:
 Every arithmetic average of any three consecutive strength tests equals or exceeds fc’.
 No individual strength test (average of two cylinders) falls below fc’
 by more than 3.5 MPa (500 psi) when fc’ is 35 MPa (5000 psi) or less; or
 by more than 0.10fc’ when fc’ is more than 35 MPa
Example
For Required fc’ = 20 MPa, if following are the test results of 7 samples
Mean 1 = (19 + 20 + 22) / 3 = 20.33 MPa
Mean 2 = (20 + 22 + 23) / 3 = 21.67 MPa
Mean 3 = (22 + 23 + 19) / 3 = 21.33 MPa
Mean 4 = (23 + 19 + 18) / 3 = 20.00 MPa
Mean 5 = (19 + 18 + 24) / 3 = 20.33 MPa
Considering these two point the quality of concrete is acceptable
Mix Design
 Ingredients of concrete are mixed together in order to get a specified Required Average Strength, fcr’ .
 If we use fc’ as target strength during mix design the average strength achieved may fall below fc’.
 To avoid understrength concrete fcr’ is used as target strength inplace of fc’.
fcr’ > fc’
ACI5.3.2 Required Average Compressive Strength
Table 5.3.2.1Required Average Compressive Strength when Data are Available to Establish a Sample Standard Deviation
Specified Compressive Strength, f_{c}’ (MPa)  Required Average Strength, f_{cr}’ (MPa) 
f_{c}’ ≤ 35  Larger of value computed from Eq. (51) & (52) 
f_{cr}’ = fc’ + 1.34 S_{s}_{ }(51)  
f_{cr}’ = f_{c}’ + 2.33 S_{s }– 3.45_{ }(52)  
f_{c}’ > 35  Larger of value computed from Eq. (51) & (53) 
f_{cr}’ = fc’ + 1.34 S_{s}_{ }(51)  
f_{cr}’ = 0.9fc’ + 2.33 S_{s }(53) 
Table 5.3.2.2Required Average Compressive Strength when Data Are Not Available to Establish a Sample Standard Deviation
Specified Compressive Strength, f_{c}’ (MPa)  Required Average Strength, f_{cr}’ (MPa) 
f_{c}’ < 21  f_{cr}’ = fc’ + 7_{ } _{ } 
21≤ f_{c}’ ≤ 35  f_{cr}’ = fc’ + 8.5 
f_{c}’ > 35  f_{cr}’ = 1.1fc’ + 5 
Stress Strain Curve of Concrete
Modulus of Elasticity
Concrete is not an elastic material therefore it does not have a fixed value of modulus of elasticity
Secant modulus (Ec)
is the one which is being used in design.
Ec = 0.043 wc1.5√fc’
wc = density of concrete in kg/m3
fc’ = specified cylinder strength in MPa
For normal weight concrete, say wc = 2300 kg/m3
Ec = 4700√fc’
Reinforcing Steel
Steel bars are:
 Plain
 Deformed (currently in use)
Deformed bars have longitudinal and transverse ribs. Ribs provide a good bond between steel and concrete. If this bond fails steel becomes in effective.
The most important properties for reinforcing steel are:
 Young’s modulus, E (200 GPa)
 Yield strength, fy
 Ultimate strength, fu
 Size and diameter of bar
hi
i am looking forward for ultimate tensile strain of plain concrete.
however, i would like to know as HOW to plot the tensile part of stress and strain curve of concrete with reference of tangent modulus or secant modulus.
These Experiments are to be uploaded on our site.