Plain and Reinforced Concrete Theory

1. ACI 318-05 By American Concrete Institute. For general concrete constructions (buildings)
2. AASHTO Specifications for Concrete Bridges. By American Association of State Highway  and Transportation Officials.
3. ASTM (American Standards for Testing and Materials)  for testing of materials.

• 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 (un-factored)  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

Strength Reduction Factor / Resistance Factor, Φ

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.

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 10-6 per MPa
Creep Strain = 10 x 116 x 10-6 = 116 x 10-5
Shortening due to creep =  3000 x 116 x 10-5   = 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.

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

19, 20, 22, 23, 19, 18, 24 MPa
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

1.Every arithmetic average of any three consecutive strength tests equals or exceeds fc’.

2.None of the test results fall below required fc’ by 3.5 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 under-strength concrete fcr’ is used as target strength in-place of fc’.

fcr’ > fc’
ACI-5.3.2 Required Average Compressive Strength

Table 5.3.2.1-Required Average Compressive Strength when Data are Available to Establish a Sample Standard Deviation

Specified Compressive Strength, fc’ (MPa)	Required Average Strength, fcr’ (MPa)
fc’ ≤ 35	Larger of value computed from Eq. (5-1) & (5-2)
	fcr’  = fc’  + 1.34 Ss                        (5-1)
	fcr’ = fc’  + 2.33 Ss – 3.45        (5-2)
fc’ > 35	Larger of value computed from Eq. (5-1) & (5-3)
	fcr’ = fc’  + 1.34 Ss                         (5-1)
	fcr’ = 0.9fc’  + 2.33 Ss               (5-3)

Table 5.3.2.2-Required Average Compressive Strength when Data Are Not Available to Establish a Sample Standard Deviation

Specified Compressive Strength, fc’ (MPa)	Required Average Strength, fcr’ (MPa)
fc’ < 21	fcr’  = fc’  + 7
21≤ fc’ ≤ 35	fcr’ = fc’  + 8.5
fc’ > 35	fcr’ = 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

 

Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete, Plain and Reinforced Concrete