CEE 4511
Design of Reinforced Concrete Structures I
Concrete is the second most consumed
materials in the world after water.
33 billion tons of concrete is produced
every year (11 kg/person/day).
The ingredients of concrete are collected
from the natural resources. Need to think
about sustainability of construction
materials.
Structure of Concrete Matrix
Stone
Sand
Cement
paste
Cross section (10×10cm )
Interfacial Transition Zone (ITZ)
Concrete is a stone-like material obtained
from a mixture of cement, sand, gravel, and
water.
•Cement – binder material (15%)
•Water – hydrate cement, and also gives
workability (10%)
•Aggregate – Sand (FA), Gravel/Stone
Chips/Brick Chips (Khoa) (CA) (75%)
Cement
•1824
•Binder of concrete
•C3S, C2S, C3A, C4AF
•Reacts with water and produce binding property
•Fineness of cement
•Setting (Initial Setting Time and Final Setting Time)
•Different Types of Cement (OPC, Blended, Composite, Fly
Ash cement, etc.)
•Heat of Hydration
Hydration Reactions of Cement:
2 (C3S) + 6 H C3S2H3 + 3 Ca(OH)2
2 (C2S) + 4 H C3S2H3 + Ca(OH)2
C 3A + 6 H C3AH6
C4AF+2 Ca(OH)2 + 10 H C3AH6 + C3FH6
C = CaO, S = SiO2’ H = H2O, A =Al2O3, F = Fe2O3
C3A + 2CaSO4.2H2O+32 H 3CaO.Al2O3. 3CaSO4.32H2O
Ettringite
Monosulphate
(stable in sulfate deficient
situation)
We need water for hydration of cement, the
remaining water will create voids
Progress of hydration
Gel with C3S2H3,C3AH6,Ca(OH)2
Aggregate
75% of mass of concrete is aggregate
Coarse Aggregate
Fine Aggregate
Grading of Aggregate
Types of Aggregate
Grading Curve
FM
Absorption Capacity
Stone
Cross section (10×10cm )
Sand
Cement
paste
Maximum size of coarse aggregate
•Should not be more than 1/5th of the
narrowest dimension
•Should not be more than 1/3rd of the slab
thickness
•Should not be more than 3/4th of minimum
distance between reinforcements.
(Size of cylinder specimens)
(Cover concrete)
Unsieved Coarse Aggregate
More
water in
sand
Strength
&
Durability
Over Saturated FA
Controlled Grading…ASTM C33
Over 25 mm
Over 20 mm
5%
Over 10 mm Over 5 mm
57.5% 37.5%
SSD Sand
ASTM C 150 OPC
ASTM C 595 Blended Hydraulic Cement
Admixtures ASTM C 494 Chemical Admixtures
(Chemical/Mineral)
Chemical admixture (Accelerator, Retarder, Water
reducer, air entraining admixture, etc.)
Less than 5% of cement mass.
Mineral Admixture (Fly ash, slag, silica fume, rice
husk ash, wheat husk ash, volcanic ash, etc.)
10 ~ 70% of cement can be replaced by fly ash or
slag or both.
Mixture Proportioning
Amount of individual ingredient of concrete (C, W, FA, and CA) for making unit
volume (say 1 m3) of concrete.
Key Parameters: water to cement ratio, cement content, sand to aggregate volume
ratio, specific gravity of the ingredients, slump, maximum aggregate size, strength
requirement.
Volume of Air
Volume of Water
Volume of Cement
1 m3
Volume of Aggregates (FA and CA)
A dense mixture will give more strength.
Grading of aggregate is very important.
A + S + W + C + Air%=1
a s w c
S s =.44
S s + A a
Assumed 1~2% air voids in concrete (non air-entrianed concrete.
Solving the above equations, the amounts of FA
(sand) and CA (khoa) per cubic meter of concrete
were obtained.
Volumetric Mix Proportion
Commonly used in Bangladesh.
1:1.5:3 (C:S:CA)…….f’c= 3000 ~ 3500 psi
1:2:4 (C:S:CA)………f’c= 2500 ~ 3000 psi
W/C=0.5 as per BNBC 2006.
Mixing, Compaction, Curing
Proper mixing is important.
Proper compaction is important.
Curing should be done carefully immediately
after placement of concrete.
70% of concrete strength is developed by
the 1st week. Therefore, curing of concrete
should be ensured at the very early stage.
Workability of concrete
Slump Test
Flow Test – SCC (flow diameter)
Compressive Strength
Well Curing
Poor Curing Durability
& strength
No curing
Time
Compressive Strength
14000
100
Compressive strength - MPa
12000
80
10000
60 8000
Psi
6000
40
4000
20
2000
0
.25 .35 .45 .55 .65 .75
W/C
100 120
Water Permeability 10-12 cm/s
80
60
20 40
.3 .4 .5 .6 .7 .8
W/C
Water plays an important role to the strength and durability of concrete.
Splitting Test
Splitting Tensile Strength
Modulus of Rupture
Modulus of rupture is higher than the splitting tensile strength.
1 gallon = 3.7853 liter (US)
1 gallon = 4.55 liter (British)
Concrete – very weak in tension
Tensile strength = one-tenth of compressive strength.
ft = 6 ~ 7 f '
c
Stress and Strain – Different Loading Rate
Rate of loading – 35 psi/sec (as per ASTM standard)
Sharp failure
surface for
HSC.
Young’s Modulus of Concrete
Ec = 57000 f c
'
For normal sand-and-stone concrete, Wc=145 pcf
Creep of Concrete
Creep Strain
Creep Coefficient =
Initial Elastic Strain
Cct = Creep coefficient at
time t (in days after
loading)
Ccu = Ultimate creep
coefficient
f’c Creep Coefficient
3000 psi 3.1
6000 psi 2.4
8000 psi 2.0
Shrinkage of Concrete
Tests, Quality Control, and Inspection
ASTM standards are used.
6 inch by 12 inch concrete cylinder or 6 inch cubes (at least 2 samples).
4 inch by 8 inch concrete cylinder or 4 inch cubes (at least 3 samples).
Cylinder strength = 0.85 Cube Strength
Dispersion of test data are to be considered.
Loading rate – 35 psi/s; Capping - Sulfur mortar capping , Neat
Cement Paste (NCP), Neoprene Pad, Water saturated condition,
Test result – nearest 10 psi.
Characteristic strength
Characteristic strength is defined as that level of strength below which a
specified proportion of all valid test results is expected to fail. Unless
otherwise stated, this proportion is taken to be 5%.
Due to the variability of constituent materials and testing, the concrete must
be designed to meet a target mean strength, i.e. a margin above the
characteristic strength is required to give a 95% confidence in achieving the
characteristic. The margin is based on 1.64 standard deviations (sd).
Specified/Design Strength and Required Strength
Required strength will depend on the dispersion of data (standard deviation)
ACI 318 – Building Code Requirement for Structural Concrete and
Commentary (New Version) – 318-14
Minimum Number of Data = 30
Standard Deviation
The tests must represent concrete with (1) a specified compressive strength within
1000 psi of f’c for the project, and (2) materials, qulaity control, and conditions
similar to those expected for the project in question.
If fewer than 30 but at least 15 tests are available, the equation may still be used,
but statbdard deviation must be multiplied by a factor as shown in the following
table:
If fewer than 15 test have been made, the average strength must exceed f’c by at
least 1000 psi for f’c less than or equal to 3000 psi; by at least 1200 psi for f’c
bewteen 3000 to 5000 psi; and by 0.1f’c+700 psi for f’c over 5000 psi (as per ACI
Code).
Design Strength average Comment
4000 psi 1 4730 psi over 3500 psi OK
2 4280 psi over 3500 psi OK 4316.666667 1,2,3 OK
3 3940 psi over 3500 psi OK 4196.666667 2,3,4 OK
f'c=4000 psi 4 4370 psi over 3500 psi OK 4496.666667 3,4,5 OK
5 5180 psi over 3500 psi OK 4806.666667 4,5,6 OK
6 4870 psi over 3500 psi OK 4993.333333 5,6,7 OK
7 4930 psi over 3500 psi OK 4883.333333 6,7,8 OK
8 4850 psi over 3500 psi OK
Data points are less than 15
Required Strength 5200 psi
Average of 8 data 4643.75 psi Less than the Required Strength
Need to increase the strength by changing mix design of concrete
Steel
Deformed Bars
(Plain bars (without any
deformation on the
surface) were
used before)
Bangladesh
500 DWR
420
400
600 DR
Reinforced Concrete Flexural Cracks (bending
stress (tension) at the
bottom face)
Reinforcements
(to take
tension and to
prevent
collapse of the
beam)
Concrete is weak in tension. Therefore, to carry the tensile forces of the
structural members, reinforcements (steel) are used. Reinforcements
are also used to carry the compression forces in structural members.
Cantilever Beam
Fixed Ended Beam
Why are steels used as reinforcement?
1. Steel and concrete have similar thermal expansion coefficent (for
concrete 5.5 ~ 7.5 x 10-6 /oF and for steel 6.5 X10-6/oF).
Negligible forces between steel and concrete will be developed due
to the change in temperature.
2. Good bonding between steel and concrete prevents slip of the steel
bars relative to the concrete
3. A protection film is developed over the steel bars in concrete which
prevents steel from corrosion inside concrete.
4. When concrete is crushed at strain level of 0.002 ~ 0.003, steel
yields.
Advantages and limitations of reinforced concrete
Learn by yourselves.
Application of Reinforced Concrete
One way slab
One way joist floor with closely spaced ribs
Flat Plate
Flat Plate with Column Capital
Folded Plate
Cylindrical Shell Roof
Spherical Shell
Cable Stayed Bridge
Box Girder Bridge
Concrete Arch Bridge
Circular Concrete Tank
Simple Structural Beam
A City of RC
Osaka, Japan
Tower
Suspension Bridge
RC Bridge
Gravity Dam
Arch Dam
Storage Tank
Ribbed Floor
Beam and
Girder Floor
Rigid Frame
Flat Slab
Folded Plate
Cylindrical
Roof
Shell Roof
Multiple Arch
Bridge
Storage Tank
Shell Roof
Counterfort
Rigid Frame
Retaining
Bridge
Wall
Hyperbolic Dome Roof
Shell
Prestressed Concrete
(Pre-tensioned and post-
tensioned)
Prestressed Concrete – Main Features
• Full section of concrete is under compression
before imposing service load to avoid
cracking of concrete.
• Effective utilization of materials.
• Need high strength concrete and high grade
steel bars to reduce losses of pre-stress.
• Good for long span.
Prestressing Steel…Need very high grade steel
Relaxation of Steel
Pre-stress at time t Initial pre-stress
Yield Strength of
prestressing steel
Large initial stress….more
loss due to relaxation
Time (Hours)
Topics learned from Chapter 1
Concrete and its basic properties
Quality control of concrete
Different factors related to strength of concrete
Tests for compressive strength/tensile strength/modulus of rupture/Modulus
of Elasticity
Different relationships
Mix design of concrete
Required strength and design strength
Problems related to required strength and design strength
Steel…its properties…
Different sizes of steel bars and its areas
Pre-stressed concrete
