rcc details
TRANSCRIPT
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Reinforced Cement Concrete (RCC)
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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 fordifferent civil engineering structures
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Introductory Lectures
Structural concreteconcrete and steel
Complimentary properties
- Concreteresists compression- Steel resists tension in most cases
Structural concreteplain, reinforced,
prestressed.
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Code of Practice
Designers guided by guidelines andspecifications 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 318-
ACI 318 or ACI code
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Code of PracticeACI code
Unified Design Method (UDM) is based on
strength of structural members assuming
failure conditioncrushing strength of
concrete or yield of reinforcing bars
Actual loads or working loads are multiplied
by load factors to obtained factored design
loads
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Limit State design
3 limit states have to be analyzed in this
method
- Load carrying capacity(safety, stability
- deformation ( deflections, vibrations)
- crack formation
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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.
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Loads
Members design to resist loads
Two types of loads
- Dead Loadsweight of structure and otherelements placed on ittiles, roofing , walls
- Live Loadssteady / unsteady , slowly or
/rapidly, laterally or vertically - weight ofpeople, furniture, wind, temperature,
earthquake etc.
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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
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Safety Provisions
Structural Members designed for higher loadsthan 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 loadfactors compared to Live loads.
Several load combinations have to be alsoconsidered to design the structure for differentload combinations
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Strength Reduction Factor
ACI provides for
strength reduction factor to reduce the
strength to account for degree of accuracy to
which strength is estimated, variations on
materials and dimensions and other factors
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Part -2 Basics of Concrete and
Steel
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Basics of Cement Concrete
Cement Concrete made up of
- Coarse Aggregate
- Fine Aggregate
- Cement
- Water
- Admixture
Water- Cement mix produces a paste filling voidsof aggregates producing a uniform denseconcrete
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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
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Concrete Mix
Proper proportioning of different componentsand well graded sound aggregates give strengthto concrete
Admixtures give concrete desired strength andquality
Concrete is subsequently poured using mixers,vibrated to get a dense mix at site and then curedto get concrete of desired strength and properties
Concrete strength increases with age about 70% in 7 days and 85-90 % in 14 days (28 daysstrength is a benchmark of design)
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Concrete Strength
Concrete strength is measured by testing cubes
(6)or cylinders (6x 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 6x12
cylinders
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Initial straight lineportion
Max. stress at
about 0.002 strain
Rupture at about
0.003 strain
Concrete strength3000-6000 psi (21-
42 N/mm.2)
High strength
concrete recently
used
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Concrete Strength and Modulus
Tensile strength of concrete is low compared tocompressive strength
Flexural strength is 10-20 % of compressivestrength
ModularRatio , Es / Ecplays an important rolein design of RCC elements
The ACI Code allows the use of
Ec= 57,000 fc (psi) = 4700 fc Mpa
Poissonsratio:- transverse to longitudinal strain0.15 to 0.20 average 0.18
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Stress Strain Curves for Steel
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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
106psi (2.0 x 105MPa)
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Part -3
Flexure Analysis of RCC Beams
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Flexure Analysis of RCC Beams
The analysis and design of a structural member may beregarded 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 asbending moments, shear, torsion, or axial forces depending
on how these loads are applied to the structure
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Flexure Analysis
In proportioning reinforced concrete structuralmembers, 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
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Flexure Analysis
3. Control of cracking conditions under service loads.
Visible cracks spoil the appearance of the structure andalso 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. (0.33mm) for exterior members.
Control of cracking is achieved by adopting and limitingthe spacing of the tension bars
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Assumptions
RCC sections are non-homogenous since thesection is made up of two materialsconcreteand steel
Proportioning ( determining sizes and areasof each component) by ultimate strength isbased on assumptions
These assumptions make the design simpler-but their validity needs to be checked andkept in mind
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Assumptions
1. Strain in Concrete is the same as that inreinforcing steel at that level this willhappen provided the bond is adequate
2. Strain in concrete is proportional to thedistance from the neutral axis
3. The modulus of elasticity of all grades of steelis taken as E, = 29 x106lb./in2( 200,000 MPaor N/mm.2 )The stress in the elastic range isequal to the strain multiplied by Es
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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
http://en.wikipedia.org/wiki/File:Beam_bending.pnghttp://en.wikipedia.org/wiki/File:Beam_bending.png -
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Assumptions
4. Plane cross-sections continue to be plane afterbending.
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 iseffective in resisting the external moment.
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Assumptions
6. At failure the maximum strain at the extremecompression fibres is assumed equal to 0.003- ACI Code provision
7. For design strength, the shape of thecompressive concrete stress distribution maybe assumed to be rectangular, parabolic, ortrapezoidal. In this course, a rectangular
shape will be assumed (ACI Code, Section10.2)
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Behavior of Simply Supported RCC
Beam Loaded to Failure
Concrete being weakest in tension, a concrete beamunder an assumed working load will definitely crack atthe tension side, and the beam will collapse if tensilereinforcement is not provided
Concrete cracks occur at a loading stage when itsmaximum tensile stress reaches the modulus ofrupture of concrete
Therefore, steel bars are used to increase the moment
resisting capacity of the beam; the steel bars resist thetensile force, and the concrete resists the compressiveforce
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Behavior of a RC beam to failure
To study the behaviour of a reinforced concrete beamunder increasing load, let us examine how two beams weretested to failure. Details of the beams are shown in Fig.
Both beams had a section of 4.5 in. by 8 in. (110 mm. by200 mm), reinforced only on the tension side by two no. 5bars. They were made of the same concrete mix. Beam 1had no stirrups, whereas beam 2 was provided withreinforcement no. 3, stirrups, spaced at 3 in
The loading system and testing procedure were the samefor both beams. To determine the compressive strength ofthe concrete and its modulus of elasticity, Ec, a standardconcrete cylinder was tested, and strain was measured atdifferent load increments
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Behavior of RC beam to Failure
Stage 1
At zero external load, each beam carried its own weight in addition to thatof 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 steelreinforcement, resisted the bending moment and shearing forces.
Maximum stress occurred at the section of maximum bending moment-thatis, at midspan. Maximum tension stress at the bottom fibers was much lessthan the modulus of rupture of concrete.
Compressive stress at the top fibers was much less than the ultimateconcrete compressive stress, fc. No cracks were observed at this stage.
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Behavior of RC beam to failure Stage 3 contd. Load increase beyond P1
In general, the development of cracks and the spacing andmaximum width of cracks depend on many factors, such asthe level of stress in the steel bars, distribution of steel barsin 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 loadwas again increased, new cracks developed, extendingtoward the supports.
The spacing of these cracks depends on the concrete coverand the level of steel stress. The width of cracks alsoincreased.
One or two of the central cracks were most affected by theload, and their crack widths increased appreciably, whereas
the other crack widths increased much less.
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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 obtainedby multiplying the strain of steel, by Es, the modulus of
elasticity of steel.
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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. BalancedSection
3. Compression controlled (also called Over
Reinforced)
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Tension Controlled Section
Steel may reach its yield strength before theconcrete reaches its maximum strength, Fig.3.3 a.
In this case, the failure is due to the yielding ofsteel reaching a high strain equal to or greaterthan 0.005.
The section contains a relatively small amountof steel and is called a tension-controlledsection.
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Stress Strain Curves for Steel
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Fig. 3.3 a
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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.
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Fig. 3.3 b
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Compression Controlled Section
Concrete may fail before the yield of steel, Fig.3.3 c, due to the presence of a high percentage ofsteel in the section. In this case, the concretestrength and its maximum strain of 0.003 arereached, but the steel stress is less than the yieldstrength, that is, fsis less than fy.
The strain in the steel is equal to or less than
0.002. This section is called a compression-controlled
section.
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Compression Controlled Section
Fig. 3c
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Choice of Type of Section
In beams designed as tension-controlled sections,steel yields before the crushing of concrete.Cracks widen extensively, giving warning beforethe concrete crushes and the structure collapses.The ACI Code adopts this type of design.
In beams designed as balanced or compression-controlled sections, the concrete fails suddenly,
and the beam collapses immediately withoutwarning. The ACI Code does not allow this type ofdesign.
Strain Limits for Tension and Tension
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Strain Limits for Tension and Tension
Controlled Sections The design provisions for both reinforced concrete
members are based on the concept of tension orcompression-controlled sections, ACI Code, Section 10.3.
Both are defined in terms of tensile strain (TS), (, in theextreme 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
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Strain Limits in Tension and Tension
Controlled Sections
Compression-controlled sections are those sections in whichthe Tensile strain, TS, in the extreme tension steel atnominal strength is equal to or less than the compressioncontrolled strain limit at the time when concrete incompression reaches its assumed strain limit of 0.003, (
concrete= 0.003).
For grade 60 steel, (fy= 60 ksi), the compression-controlledstrain limit may be taken as a net strain of 0.002, Fig. 3.4a.
This case occurs mainly in columns subjected to axial forcesand moments.
Strain in Tension and Tension
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Strain in Tension and Tension
Controlled Sections
Tension-controlled sections are those sections inwhich the TS, tensile , is equal to or greater than0.005 just as the concrete in the compressionreaches its assumed strain limit of 0.003, Fig. 3.4 c
Sections in which the TS in the extreme tensionsteel lies between the compression controlled
strain limit (0.002 for f , = 60 ksi) and the tension-controlled strain limit of 0.005 constitute thetransition region, Fig. 3.4b.
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Strain levels
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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 s = fy/Es just as the maximum
strain in concrete at the extreme compression
fibers reaches 0.003, Fig. 3.5.
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Load Factors
Based on historical studies of various structures, experience, andthe principles of probability, the ACI Code adopts a load factor of1.2 for dead loads and 1.6 for live loads. The dead load factor issmaller, because the dead load can be computed with a greaterdegree of certainty than the live load.
The choice of factors reflects the degree of the economical designas well as the degree of safety and serviceability of the structure. Itis also based on the fact that the performance of the structureunder actual loads must be satisfactorily within specific limits.
If the required strength is denoted by U (ACI Code, Section 9.2), andthose due to wind and seismic forces are W and E, respectively,according to the ACI Code, the required strength U, shall be themost critical of the following factors (based on the ASCE 7-05)
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Load Combinations
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Strength Reduction Factor
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Strength Reduction Factors
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Analysis and Design
C i St Di t ib ti
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Compressive Stress Distribution The distribution of compressive concrete stresses at failure
may be assumed to be a rectangle, trapezoid, parabola, orany 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 insteel 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
B l d S ti
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Balanced Section
In Fig. 3.7, if concrete fails, c, = 0.003, and if
steel yields, as in the case of a balanced
section, fs= fy
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Compressive Stress Distribution
A compressive force, C, develops in the compression zoneand a tension force, T, develops in the tension zone at thelevel of the steel bars.
The position of force T is known, because its line of
application coincides with the center of gravity of the steelbars.
The position of compressive force C is not knownunless thecompressive volume is known and its center of gravity is
located.
If that is done, the moment arm, which is the verticaldistance between C and T, will consequently be known.
B l d S ti
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Balanced Section
In Fig. 3.7, if concrete fails, c, = 0.003, and if
steel yields, as in the case of a balanced
section, fs= fy
f l
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Compressive force location
The compression force, C, is represented bythe 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(1fc), where 1fcis an assumed
average stress of the non uniform stress
block.
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Compressive Stress Distribution BalancedS ti
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Section
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Singly Reinforced Beam Balanced
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Singly Reinforced Beam Balanced
Section
This value is equal to the area of steel, As, dividedby the effective cross-section, b* d:
b= As / b *d (For % multiply by 100)
whereb = width of the compression face of the
member
d = distance from the extreme compression
fiber to the centroid of the longitudinal
tension reinforcement
E i f A l i d D i
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Equations for Analysis and Design
Two basic equations for the analysis and design ofstructural members are the two equations ofequilibrium 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 eitherthe compressive force, C, multiplied by its arm or the
tension force, T , multiplied by the same lever arm:
Internal Moment Mn and
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Internal Moment Mn and
Bending Moment Mu
Internal Moment
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Step 1.
From the strain diagram of Fig. 3.11,
B l d S ti
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Balanced Section
B l d S ti
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Balanced Section
B l d S ti
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Balanced Section
B l d S ti St l %
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Balanced Section Steel %
Because Balanced section steel is used
Balanced Section Steel %
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Balanced Section Steel %
Internal Moment
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Internal Moment
Design Moment
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Design Moment
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Ratio of a to d
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Ratio of a to d