Reinforced Cement Concrete (RCC)
CE-217
Prof. Sharad Mhaiskar
Introductory Lectures
-1
• Design of Structures
- determine forces acting on the structure
using structural analysis
- proportion different elements economically,
stability, safety, serviceability functionality
• Structural concrete is commonly used for
different civil engineering structures
Introductory Lectures
• Structural concrete – concrete and steel
• Complimentary properties
- Concrete – resists compression
- Steel resists tension in most cases
• Structural concrete – plain, reinforced,
prestressed….
Code of Practice
• Designers guided by guidelines and
specifications called “ Code of Practice”
• Codes specified by different organizations to
ensure public safety
• Codes specify design loads, allowable stresses,
materials , construction types and other
details
• US – American Concrete Institute Code 318ACI 318 or ACI code
Code of Practice – ACI code
• Unified Design Method (UDM) is based on
strength of structural members assuming
failure condition – crushing strength of
concrete or yield of reinforcing bars
• Actual loads or working loads are multiplied
by load factors to obtained factored design
loads
Elastic Approach
• Not used in ACI or rather deleted by ACI
• Based on Elastic Theory
• Assumes a straight line stress distribution
along the depth of the concrete member
• Members are proportioned on the basis of
allowable stresses on concrete and steel
Limit State design
• 3 limit states have to be analyzed in this
method
- Load carrying capacity – (safety, stability …
- deformation ( deflections, vibrations…)
- crack formation
Units
• SI system – (System International)
• W= m g = 1 kg. x 9.81 m/s2 = 9.81 N
• 1 kN = 1000 N
• 1 m. = 100 cm.
Loads
• Members design to resist loads
• Two types of loads
- Dead Loads – weight of structure and other
elements placed on it – tiles, roofing , walls
- Live Loads– steady / unsteady , slowly or
/rapidly, laterally or vertically - weight of
people, furniture, wind, temperature,
earthquake etc.
Loads to be specified
• ACI does not specify loads
• American National Standards Institute
specifies loads
• AASHTO specifies highway and railway loading
for bridges and highways
Safety Provisions
• Structural Members designed for higher loads
than actual to have margin / safety against failure
• Multiply actual loads by load factors to get
factored loads
• Load factors depend on how accurately the loads
can be estimated – eg. Dead loads lower load
factors compared to Live loads.
• Several load combinations have to be also
considered to design the structure for different
load combinations
Strength Reduction Factor
• ACI provides for
strength reduction factor φ to reduce the
strength to account for degree of accuracy to
which strength is estimated, variations on
materials and dimensions and other factors
Part -2 Basics of Concrete and
Steel
Basics of Cement Concrete
• Cement Concrete made up of
- Coarse Aggregate
- Fine Aggregate
- Cement
- Water
- Admixture
• Water- Cement mix produces a paste filling voids
of aggregates – producing a uniform dense
concrete
Concrete Casting
•
•
•
•
Plastic Concrete placed in a mold
Cured
Left to set, harden and gain strength with time
Strength of concrete depends on many factors
a. Water Cement ratio
b. Properties and proportions of constituents
c. Method of mixing and curing
d. Age of Concrete
e. Loading Conditions
f. Shape and Dimensions of tested specimens
Concrete Mix
• Proper proportioning of different components
and well graded sound aggregates give strength
to concrete
• Admixtures give concrete desired strength and
quality
• Concrete is subsequently poured using mixers,
vibrated to get a dense mix at site and then cured
to get concrete of desired strength and properties
• Concrete strength increases with age – about 70
% in 7 days and 85-90 % in 14 days (28 days
strength is a benchmark of design)
Concrete Strength
• Concrete strength is measured by testing cubes
(6”) or cylinders (6” x 12”)
• Performance of RCC depends on relative
strength of concrete and steel
• Stress-strain behavior of both materials is
important.
• Stress-strain behavior is assessed using 6”x12“
cylinders
• Initial straight line
portion
• Max. stress at
about 0.002 strain
• Rupture at about
0.003 strain
• Concrete strength
3000-6000 psi (2142 N/mm.2)
• High
strength
concrete recently
used
Concrete Strength and Modulus
• Tensile strength of concrete is low compared to
compressive strength
• Flexural strength is 10-20 % of compressive
strength
• “Modular Ratio” , Es / Ec plays an important role
in design of RCC elements
• The ACI Code allows the use of
Ec = 57,000 √ f’c (psi) = 4700 √f’c Mpa
• Poisson’s ratio:- transverse to longitudinal strain
0.15 to 0.20 average 0.18
Steel Reinforcement
• Steel reinforcement can be of different types
- Round Bars ¼ “ to ¾” ( 6mm. To 36 mm.) and
1 ¾ “ (45 mm.) and 2 ¼ “ (57 mm.)
- Round bars can be plain or deformed (Lect.0a)
- Plain bars used for stirrups, Deformed bars
used for main reinforcement to provide
bond
Stress Strain Curves for Steel
Modulus of Elasticity of Reinforcement
• Modulus of elasticity is constant for all types
of steel
• The ACI Code has adopted a value of Es = 29 X
106 psi (2.0 x 105 MPa)
Part -3
Flexure Analysis of RCC Beams
Flexure Analysis of RCC Beams
• The analysis and design of a structural member may be
regarded as the process of selecting the proper materials
and determining the member dimensions such that the
design strength is equal or greater than the required
strength
• The required strength is determined by multiplying the
actual applied loads, the dead load, the assumed live load,
and other loads, such as wind, seismic, earth pressure, fluid
pressure, snow, and rain loads, by load factors
• These loads develop internal forces / stresses such as
bending moments, shear, torsion, or axial forces depending
on how these loads are applied to the structure
Flexure Analysis
• In proportioning reinforced concrete structural
members, three main items can be investigated:
1. The safety of the structure, which is maintained by
providing adequate internal design strength
2. Deflection of the structural member under service
loads. The maximum value of deflection must be
limited and is usually specified as a factor of the
span, to preserve the appearance of the structure
Flexure Analysis
3. Control of cracking conditions under service loads.
• Visible cracks spoil the appearance of the structure and
also permit humidity to penetrate the concrete,
causing corrosion of steel and consequently weakening
the reinforced concrete member.
• The ACI Code implicitly limits crack widths to 0.016 in.
(0.40mm) for interior members and 0.013 in. (0.33
mm) for exterior members.
• Control of cracking is achieved by adopting and limiting
the spacing of the tension bars
Assumptions
• RCC sections are non-homogenous since the
section is made up of two materials – concrete
and steel
• Proportioning – ( determining sizes and areas
of each component) by ultimate strength is
based on assumptions
• These assumptions make the design simplerbut their validity needs to be checked and
kept in mind
Assumptions
1. Strain in Concrete is the same as that in
reinforcing steel at that level – this will
happen provided the bond is adequate
2. Strain in concrete is proportional to the
distance from the neutral axis
3. The modulus of elasticity of all grades of steel
is taken as E, = 29 x106 lb./in2 ( 200,000 MPa
or N/mm.2 ) The stress in the elastic range is
equal to the strain multiplied by Es
The neutral axis is an axis in the cross section of a beam or shaft along which
there are no longitudinal stresses or strains. If the section is symmetric, isotropic
and is not curved before a bend occurs, then the neutral axis is at the geometric
centroid. All fibers on one side of the neutral axis are in a state of tension, while
those on the opposite side are in compression
Assumptions
4. Plane cross-sections continue to be plane after
bending.
5. Tensile strength of concrete is neglected because
a. concrete's tensile strength is only about 10% of its
compressive strength,
b. cracked concrete is assumed to be not effective,
and
c. before cracking, the entire concrete section is
effective in resisting the external moment.
Assumptions
6. At failure the maximum strain at the extreme
compression fibres is assumed equal to 0.003
- ACI Code provision
7. For design strength, the shape of the
compressive concrete stress distribution may
be assumed to be rectangular, parabolic, or
trapezoidal. In this course, a rectangular
shape will be assumed (ACI Code, Section
10.2)
Behavior of Simply Supported RCC
Beam Loaded to Failure
• Concrete being weakest in tension, a concrete beam
under an assumed working load will definitely crack at
the tension side, and the beam will collapse if tensile
reinforcement is not provided
• Concrete cracks occur at a loading stage when its
maximum tensile stress reaches the modulus of
rupture of concrete
• Therefore, steel bars are used to increase the moment
resisting capacity of the beam; the steel bars resist the
tensile force, and the concrete resists the compressive
force
Behavior of a RC beam to failure
• To study the behaviour of a reinforced concrete beam
under increasing load, let us examine how two beams were
tested to failure. Details of the beams are shown in Fig.
• Both beams had a section of 4.5 in. by 8 in. (110 mm. by
200 mm), reinforced only on the tension side by two no. 5
bars. They were made of the same concrete mix. Beam 1
had no stirrups, whereas beam 2 was provided with
reinforcement no. 3, stirrups, spaced at 3 in
• The loading system and testing procedure were the same
for both beams. To determine the compressive strength of
the concrete and its modulus of elasticity, Ec, a standard
concrete cylinder was tested, and strain was measured at
different load increments
Behavior of RC beam to Failure
Stage 1
At zero external load, each beam carried its own weight in addition to that
of the loading system, which consisted of an I-beam and some plates.
Both beams behaved similarly at this stage
At any section, the entire concrete section, in addition to the steel
reinforcement, resisted the bending moment and shearing forces.
Maximum stress occurred at the section of maximum bending moment-that
is, at midspan. Maximum tension stress at the bottom fibers was much less
than the modulus of rupture of concrete.
Compressive stress at the top fibers was much less than the ultimate
concrete compressive stress, f ’c . No cracks were observed at this stage.
Behavior of RC beam to failure
Stage 2.
• This stage was reached when the external load, P, was increased from 0
to P1 , which produced tensile stresses at the bottom fibers equal to the
modulus of rupture of concrete.
• At this stage the entire concrete section was effective, with the steel bars
at the tension side sustaining a strain equal to that of the surrounding
concrete
• Stress in the steel bars was equal to the stress in the adjacent concrete
multiplied by the modular ratio, n, the ratio of the modulus of elasticity
of steel to that of concrete. (n= Es / Ec - Strain same – stress not same)
• The compressive stress of concrete at the top fibers was still very small
compared with the compressive strength, f’c . The behavior of beams
was elastic within this stage of loading.
Behavior of RC beam to failure
Stage 3
• When the load was increased beyond P1, tensile stresses in concrete at
the tension zone increased until they were greater than the modulus of
rupture, and cracks developed.
• The neutral axis shifted upward, and cracks extended close to the level
of the shifted neutral axis. Concrete in the tension zone lost its tensile
strength, and the steel bars started to work effectively and to resist the
entire tensile force
• Between cracks, the concrete bottom fibers had tensile stresses, but they
were of negligible value. It can be assumed that concrete below the
neutral axis did not participate in resisting external moments
Behavior of RC beam to failure
• Stage 3 contd Load increase beyond P1
• In general, the development of cracks and the spacing and
maximum width of cracks depend on many factors, such as
the level of stress in the steel bars, distribution of steel bars
in the section, concrete cover, and grade of steel used.
• At this stage, the deflection of the beams increased clearly,
because the moment of inertia of the cracked section was
less than that of the uncracked section.
• Cracks started about the midspan of the beam, but other
parts along the length of the beam did not crack. When load
was again increased, new cracks developed, extending
toward the supports.
• The spacing of these cracks depends on the concrete cover
and the level of steel stress. The width of cracks also
increased.
• One or two of the central cracks were most affected by the
load, and their crack widths increased appreciably, whereas
the other crack widths increased much less.
.
Behavior of RC beam to failure
Stage 3 contd.
• At high compressive stresses, the strain of the concrete
increased rapidly, and the stress of concrete at any strain
level was estimated from a stress-strain graph obtained
by testing a standard cylinder to failure for the same
concrete.
• As for the steel, the stresses were still below the yield
stress, and the stress at any level of strain was obtained
by multiplying the strain of steel, by Es, the modulus of
elasticity of steel.
Types of failures and Strain Limits
Three types of flexural failure of a structural
member can be expected / designed depending
on the percentage of steel used in the section
1. Tension Controlled section (also called
“Under-Reinforced”)
2. “Balanced Section”
3. Compression controlled (also called “Over
Reinforced” )
Tension Controlled Section
• Steel may reach its yield strength before the
concrete reaches its maximum strength, Fig.
3.3 a.
• In this case, the failure is due to the yielding of
steel reaching a high strain equal to or greater
than 0.005.
• The section contains a relatively small amount
of steel and is called a tension-controlled
section.
Stress Strain Curves for Steel
Fig. 3.3 a
Balanced Section
• Steel may reach its yield strength at the same
time as concrete reaches its ultimate strength,
Fig. 3.3b. The section is called a balanced
section.
Fig. 3.3 b
Compression Controlled Section
• Concrete may fail before the yield of steel, Fig.
3.3 c, due to the presence of a high percentage of
steel in the section. In this case, the concrete
strength and its maximum strain of 0.003 are
reached, but the steel stress is less than the yield
strength, that is, fs is less than fy .
• The strain in the steel is equal to or less than
0.002.
• This section is called a compression-controlled
section.
Compression Controlled Section
Fig. 3c
Choice of Type of Section
• In beams designed as tension-controlled sections,
steel yields before the crushing of concrete.
Cracks widen extensively, giving warning before
the concrete crushes and the structure collapses.
The ACI Code adopts this type of design.
• In beams designed as balanced or compressioncontrolled sections, the concrete fails suddenly,
and the beam collapses immediately without
warning. The ACI Code does not allow this type of
design.
Strain Limits for Tension and Tension
Controlled Sections
• The design provisions for both reinforced concrete
members are based on the concept of tension or
compression-controlled sections, ACI Code, Section 10.3.
• Both are defined in terms of tensile strain (TS), (ε, in the
extreme tension steel at nominal strength)
• Moreover, two other conditions may develop:
(1) the balanced strain condition and ,
(2) the transition region condition.
These four conditions are defined in the next few slides:
Strain Limits in Tension and Tension
Controlled Sections
Compression-controlled sections are those sections in which
the Tensile strain, TS, in the extreme tension steel at
nominal strength is equal to or less than the compression
controlled strain limit at the time when concrete in
compression reaches its assumed strain limit of 0.003, (ε
concrete = 0.003).
For grade 60 steel, (fy = 60 ksi), the compression-controlled
strain limit may be taken as a net strain of 0.002, Fig. 3.4a.
This case occurs mainly in columns subjected to axial forces
and moments.
Strain in Tension and Tension
Controlled Sections
Tension-controlled sections are those sections in
which the TS, ε tensile , is equal to or greater than
0.005 just as the concrete in the compression
reaches its assumed strain limit of 0.003, Fig. 3.4 c
Sections in which the TS in the extreme tension
steel lies between the compression controlled
strain limit (0.002 for f , = 60 ksi) and the tensioncontrolled strain limit of 0.005 constitute the
transition region, Fig. 3.4b.
Strain levels
Balanced Section
The balanced strain condition develops in the
section when the tension steel, with the first
yield, reaches a strain corresponding to its yield
strength, fy , or εs = fy/Es just as the maximum
strain in concrete at the extreme compression
fibers reaches 0.003, Fig. 3.5.
Load Factors
• For the design of structural members, the factored design
load is obtained by multiplying the dead load by a load
factor and the specified live load by another load factor
• The magnitude of the load factor must be adequate to limit
the probability of sudden failure and to permit an
economical structural design
• The choice of a proper load factor or a proper factor of
safety depends mainly on the importance of the structure
(whether a courthouse or a warehouse), the degree of
warning needed prior to collapse, the importance of each
structural member (whether a beam or column), the
expectation of overload, the accuracy of artisanry,
and
the accuracy of calculations
Load Factors
• Based on historical studies of various structures, experience, and
the principles of probability, the ACI Code adopts a load factor of
1.2 for dead loads and 1.6 for live loads. The dead load factor is
smaller, because the dead load can be computed with a greater
degree of certainty than the live load.
• The choice of factors reflects the degree of the economical design
as well as the degree of safety and serviceability of the structure. It
is also based on the fact that the performance of the structure
under actual loads must be satisfactorily within specific limits.
• If the required strength is denoted by U (ACI Code, Section 9.2), and
those due to wind and seismic forces are W and E, respectively,
according to the ACI Code, the required strength U, shall be the
most critical of the following factors (based on the ASCE 7-05)
Load Combinations
Load Combinations
Strength Reduction Factor
Strength Reduction Factors
Analysis and Design
Compressive Stress Distribution
• The distribution of compressive concrete stresses at failure
may be assumed to be a rectangle, trapezoid, parabola, or
any other shape that is in good agreement with test results.
• When a beam is about to fail, the steel will yield first if the
section is under-reinforced, and in this case the stress in
steel is equal to the yield stress.
• If the section is over-reinforced, concrete crushes first and
the strain is assumed to be equal to 0.003
Balanced Section
• In Fig. 3.7, if concrete fails, εc, = 0.003, and if
steel yields, as in the case of a balanced
section, fs = fy
Compressive Stress Distribution
• A compressive force, C, develops in the compression zone
and a tension force, T, develops in the tension zone at the
level of the steel bars.
• The position of force T is known, because its line of
application coincides with the center of gravity of the steel
bars.
• The position of compressive force C is not known unless the
compressive volume is known and its center of gravity is
located.
• If that is done, the moment arm, which is the vertical
distance between C and T, will consequently be known.
Balanced Section
• In Fig. 3.7, if concrete fails, εc, = 0.003, and if
steel yields, as in the case of a balanced
section, fs = fy
Compressive force location
• The compression force, C, is represented by
the volume of the stress block, which has the
non uniform shape of stress over the
rectangular hatched area of bc.
• This volume may be considered equal to
C = bc(α1f’c), where α1f’c is an assumed
average stress of the non uniform stress
block.
Compressive Force Diagram
• The position of compression force C is at a
distance z from the top fibers, which can be
considered as a fraction of the distance c (the
distance from the top fibers to the neutral axis),
and z can be assumed to be equal to α2c, where
α2 < 1. The values of α1 and α2 have been
estimated from many tests, and their values, as
suggested by Mattock, Kriz, and Hognestad ,
are as follows and also adopted by ACI:
Compressive Stress Distribution Balanced
Section
SINGLY REINFORCED RECTANGULAR
SECTION IN BENDING
• Balanced condition is achieved when steel
yields at the same time as the concrete fails,
and that failure usually happens suddenly.
• This implies that the yield strain in the steel is
reached (εy = fy/ES,) and that the concrete has
reached its maximum strain of 0.003.
• The percentage of reinforcement used to
produce a balanced condition is called the
balanced steel ratio, ρb.
Singly Reinforced Beam – Balanced
Section
• This value is equal to the area of steel, As, divided
by the effective cross-section, b* d:
ρb = As / b *d (For % multiply by 100)
where
b = width of the compression face of the
member
d = distance from the extreme compression
fiber to the centroid of the longitudinal
tension reinforcement
Equations for Analysis and Design
• Two basic equations for the analysis and design of
structural members are the two equations of
equilibrium that are valid for any load and any section:
1. The compression force should be equal to the
tension force
2. The internal bending moment, Mn, is equal to either
the compressive force, C, multiplied by its arm or the
tension force, T , multiplied by the same lever arm:
Internal Moment Mn and
Bending Moment Mu
• Internal Moment
Balanced Section
• Let us consider the case of a balanced section,
which implies that at ultimate load the strain
in concrete equals 0.003 and that of steel
equals the first yield stress at distance dt
divided by the modulus of elasticity of steel,
fy /ES,
• Step 1.
From the strain diagram of Fig. 3.11,
Balanced Section
Balanced Section
Balanced Section
Balanced Section Steel %
• Because Balanced section steel is used
Balanced Section Steel %
Internal Moment
Design Moment
Ratio of ‘a’ to ‘d’