Lean Construction

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By Dr. Attaullah ShahSwedish College of
Engineering and Technology Wah Cantt.
Reinforced Concrete Design-I

• Lec-07
• Bond and Development Length

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• The basic assumption of the RCC design is that
  the strain in concrete and reinforcing steel is
  the same. If the reinforcing steel slips at its
  ends, this is not valid. Hence it must be ensured
  that sufficient bond strength is developed at the
  interface of steel and concrete to avoid slippage
  of the steel.

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Bond Strength and Development length

• Two types of bond failure can be expected in
  reinforcing bars
• Direct pull out of the steel bars, when ample
  concrete confinement is provided in the form of
  large spacing of bars or large concrete cover
• Splitting of concrete along the bar when cover
  confinement or bar spacing is insufficient

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b. Actual Distribution of Flexural Bond Stress

• Pure bending case
• Concrete fails to resist tensile stresses only
  where the actual crack is located. Steel T is
  maximum and
• T max M / jd .
• Between cracks , concrete does resist moderate
  amount of tension introduced by bond.
• u is proportional to the rate of change of bar
  force, and highest where the slope of the steel
  force curve is greatest.
• Very high local bond stress adjacent to the
  crack.

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• Beam under transverse loads,
• According to simple crack sectional theory, T is
  proportional to the moment diagram and u is
  proportional to shear force diagram.
• In actual, T is less than the simple analysis
  prediction everywhere except at the actual
  cracks.
• Similarly, u is equal with simple analysis
  prediction only at the location where slopes of
  the steel force diagrams are equals .If the slope
  is greater than assumed, bond stress is greater
  if the slope is less bond stress is less.

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ULTIMATE BOND STRENGTH AND DEVELOPMENT LENGTH

• Types of bond failure
• Direct pullout of bars
• (small diameter bars are used with
  sufficiently large concrete cover distances and
  bar spacing)
• Splitting of the concrete along the bar (cover or
  bar spacing is insufficient to resist the lateral
  concrete tension resulting from the wedging
  effect of bar deformations)

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a. Ultimate Bond Strength

• Direct pull out
• For sufficiently confined bar, adhesive bond and
  friction are overcome as the tensile force on the
  bar is increased. Concrete eventually crushes
  locally ahead of the bar deformation and bar
  pullout results.
• When pull out resistance is overcome or when
  splitting has spread all the way to the end of an
  unanchored bar, complete bond failure occurs.
• Splitting
• Splitting comes from wedging action when the ribs
  of the deformed bars bear against the concrete.
• Splitting in vertical plane
• Splitting in horizontal plane frequently begins
  at a diagonal crack in connection with dowel
  action. Shear and bond failures are often
  interrelated.
• Local bond failure
• Large local variation of bond stress caused by
  flexural and diagonal cracks immediately adjacent
  to cracks leads to this failure below the failure
  load of the beam.
• Results small slip and some widening of cracks
  and increase of deflections.
• Harmless as long as the failure does not
  propagate all along the bar.
• Providing end anchorage, hooks or extended
  length of straight bar (development length
  concept)

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Consider a bar embedded in a mass of concrete
P s pdb2/4
P tLbpdb
db
Lb
t P / Lbpdb lt tmax
s P/ pdb2/4 lt smax
P lt tmax Lbpdb
P lt smax pdb2/4
To force the bar to be the weak link tmax
Lbpdb gt smax pdb2/4
Lb gt (smax / tmax) db/4
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Development Length

• Ld development length
• the shortest distance over which a bar can
  achieve its full capacity
• The length that it takes a bar to develop its
  full contribution to the moment capacity, Mn

Ld
Mn
0
Cc
Mn (C or T)(dist)
Ts
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Steel Limit, smax

• Using the bilinear assumption of ACI 318
• smax fy
• Lb gt (fy / tmax) db/4
• Lb gt fy db / (4tmax)

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Concrete Bond Limit, tmax

• There are lots of things that affect tmax
• The strength of the concrete, fc
• Type of concrete (normal weight or light weight)
• The amount of concrete below the bar
• The surface condition of the rebar
• The concrete cover on the bar
• The proximity of other bars transferring stress
  to the concrete
• The presence of transverse steel

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Concrete Strength, fc

• Bond strength, tmax, tends to increase with
  concrete strength.
• Experiments have shown this relationship to be
  proportional to the square root of fc.

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Type of Concrete

• Light weight concrete tends to have less bond
  strength than does normal weight concrete.
• ACI 318-08 introduces a lightweight concrete
  reduction factor, l, on sqrt(fc) in some
  equations.
• See ACI 318-08, 8.6.1 for details

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Amount of Concrete Below Bars

• The code refers to top bars as being any bar
  which has 12 inches or more of fresh concrete
  below the bar when the member is poured.
• If concrete gt 12 then consolidation settlement
  results in lower bond strength on the bottom side
  of the bar
• See ACI 318-08, 12.2.4(a)

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Surface Condition of Rebar

• All rebar must meet ASTM requirements for
  deformations that increase pullout strength.
• Bars are often surface coated is inhibit
  corrosion.
• Epoxy Coating ? The major concern!
• Galvanizing
• Epoxy coating significantly reduces bond strength
• See ACI 318-08, 12.2.4(b)

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Proximity to Surface or Other Bars

• The size of the concrete cylinder tributary to
  each bar is used to account for proximity of
  surfaces or other bars.

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Presence of Transverse Steel

• The bond transfer tends to cause a splitting
  plane
• Transverse steel will increase the strength of
  the splitting plane.

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b. Development Length

• Development length is the length of embedment
  necessary to develop the full tensile strength of
  bar, controlled by either pullout or splitting.
• In Fig., let
• maximum M at a and zero at support
• fs at a? T Ab fs _
• Development length concept ?total tension force
  must be transferred from the bar to the concrete
  in the distance l by bond stress on the
  surface.
• To fully develop the strength ? T Ab fy
• ? ld
  , development length
• Safety against bond failure the length of the
  bar from any point of given steel stress to its
  nearby end must be at least equal to its
  development length. If the length is inadequate,
  special anchorage can be provided.

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ACI CODE PROVISION FOR DEVELOPMENT OF TENSION
REINFORCEMENT

• Limit
• (c ktr) / db 2.5 for pullout case
• vfc are not to be greater than 100 psi.

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For two cases of practical importance, using (c
ktr) / db 1.5,
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Example
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• Continue

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Continue
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ANCHORAGE OF TENSION BARS BY HOOKS
In the event that the desired tensile stress in a
bar can not be developed by bond alone, it is
necessary to provide special anchorage at the end
of the bar.
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b. Development Length and Modification Factors
for Hooked Bars
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Example
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ANCHORAGE REQUIREMENTS FOR WEB REINFORCEMENT
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DEVELOPMENT OF BARS IN COMPRESSION

• Reinforcement may be required to develop its
  compressive strength by embedment under various
  circumstances.
• ACI basic development length in compression
• ldb 0.02db fy/vfc

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Determining Locations of Flexural Cutoffs
Given a simply supported beam with a distributed
load.
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Determining Locations of Flexural Cutoffs
Note Total bar length Fully effective length
Development length
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Determining Locations of Flexural Cutoffs
ACI 12.10.3 All longitudinal tension bars must
extend a min. distance d (effective depth of
the member) or 12 db (usually larger) past the
theoretical cutoff for flexure (Handles
uncertainties in loads, design approximations,etc.
.)

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Determining Locations of Flexural Cutoffs
Development of flexural reinforcement in a
typical continuous beam. ACI 318R-02 - 12.10
for flexural reinforcement

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Bar Cutoffs - General Procedure
Determine theoretical flexural cutoff points for
envelope of bending moment diagram. Extract the
bars to satisfy detailing rules (from ACI Section
7.13, 12.1, 12.10, 12.11 and 12.12) Design extra
stirrups for points where bars are cutoff in zone
of flexural tension (ACI 12.10.5)
1. 2. 3.
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Bar Cutoffs - General Rules
All Bars Rule 1. Rule 2.
Bars must extend the longer of d or 12db past the
flexural cutoff points except at supports or the
ends of cantilevers (ACI 12.11.1)
Bars must extend at least ld from the point of
maximum bar stress or from the flexural cutoff
points of adjacent bars (ACI 12.10.2 12.10.4 and
12.12.2)
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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Simple Supports At least one-third of the
  positive moment reinforcement must be extend 6
  in. into the supports (ACI 12.11.1).
• Continuous interior beams with closed stirrups.
  At least one-fourth of the positive moment
  reinforcement must extend 6 in. into the support
  (ACI 12.11.1 and 7.13.2.3)

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Continuous interior beams without closed
  stirrups. At least one-fourth of the positive
  moment reinforcement must be continuous or shall
  be spliced near the support with a class A
  tension splice and at non-continuous supports be
  terminated with a standard hook. (ACI 7.13.2.3).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Continuous perimeter beams. At least one-fourth
  of the positive moment reinforcement required at
  midspan shall be made continuous around the
  perimeter of the building and must be enclosed
  within closed stirrups or stirrups with 135
  degree hooks around top bars. The required
  continuity of reinforcement may be provided by
  splicing the bottom reinforcement at or near the
  support with class A tension splices (ACI
  7.13.2.2).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 3.

• Structural Integrity
• Beams forming part of a frame that is the primary
  lateral load resisting system for the building.
  This reinforcement must be anchored to develop
  the specified yield strength, fy, at the face of
  the support (ACI 12.11.2)

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 4.

• Stirrups
• At the positive moment point of inflection and at
  simple supports, the positive moment
  reinforcement must be satisfy the following
  equation for ACI 12.11.3. An increase of 30 in
  value of Mn / Vu shall be permitted when the ends
  of reinforcement are confined by compressive
  reaction (generally true for simply supports).

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Bar Cutoffs - General Rules
Positive Moment Bars Rule 4.
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Bar Cutoffs - General Rules
Negative Moment Bars Rule 5.

• Negative moment reinforcement must be anchored
  into or through supporting columns or members
  (ACI Sec. 12.12.1).

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Bar Cutoffs - General Rules
Negative Moment Bars Rule 6.

• Structural Integrity
• Interior beams. At least one-third of the
  negative moment reinforcement must be extended by
  the greatest of d, 12 db or ( ln / 16 ) past the
  negative moment point of inflection (ACI Sec.
  12.12.3).

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Bar Cutoffs - General Rules
Negative Moment Bars Rule 6.

• Structural Integrity
• Perimeter beams. In addition to satisfying rule
  6a, one-sixth of the negative reinforcement
  required at the support must be made continuous
  at mid-span. This can be achieved by means of a
  class A tension splice at mid-span (ACI
  7.13.2.2).

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Moment Resistance Diagrams
Moment capacity of a beam is a function of its
depth, d, width, b, and area of steel, As. It is
common practice to cut off the steel bars where
they are no longer needed to resist the flexural
stresses. As in continuous beams positive moment
steel bars may be bent up usually at 45o, to
provide tensile reinforcement for the negative
moments over the support.
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Moment Resistance Diagrams
The nominal moment capacity of an
under-reinforced concrete beam is To determine
the position of the cutoff or bent point the
moment diagram due to external loading is drawn.
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Moment Resistance Diagrams
The ultimate moment resistance of one bar, Mnb
is The intersection of the moment resistance
lines with the external bending moment diagram
indicates the theoretical points where each bar
can be terminated.
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Moment Resistance Diagrams
Given a beam with the 4 8 bars and fc3 ksi and
fy50 ksi and d 20 in.
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Moment Resistance Diagrams
The moment diagram is
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Moment Resistance Diagrams
The moment resistance of one bar is
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Moment Resistance Diagrams
The moment diagram and crossings
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Moment Resistance Diagrams
The ultimate moment resistance is 2480 k-in. The
moment diagram is drawn to scale on the basis A
bar can be terminated at a, two bars at b and
three bars at c. These are the theoretical
termination of the bars.
a
b
c
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Moment Resistance Diagrams
Compute the bar development length is
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Moment Resistance Diagrams
The ultimate moment resistance is 2480 k-in. The
moment diagram is drawn to scale on the basis A
bar can be terminated at a, two bars at b and
three bars at c. These are the theoretical
termination of the bars.
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Moment Resistance Diagrams
It is necessary to develop part of the strength
of the bar by bond. The ACI Code specifies that
every bar should be continued at least a distance
d, or 12db , which ever is greater, beyond the
theoretical points a, b, and c. Section 12.11.1
specify that 1/3 of positive moment reinforcement
must be continuous.
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Moment Resistance Diagrams
Two bars must extend into the support and moment
resistance diagram Mub must enclose the external
bending moment diagram.
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Example Cutoff
For the simply supported beam with b10 in. d
17.5 in., fy40 ksi and fc3 ksi with 4 8 bars.
Show where the reinforcing bars can be
terminated.
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Example Cutoff
Determine the moment capacity of the bars.
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Example Cutoff
Determine the location of the bar intersections
of moments.
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Example Cutoff
Determine the location of the bar intersections
of moments.
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Example Cutoff
Determine the location of the bar intersections
of moments.
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Example Cutoff
The minimum distance is
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Example Cutoff
The minimum amount of bars are As/3 or two bars
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Example Cutoff
The cutoff for the first bar is 41 in. or 3 ft 5
in. and 18 in or 1 ft 6 in. total distance is 41
in.18 in. 59 in. or 4 ft 11 in.
Note error it is 4-11 not 5-11
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Example Cutoff
The cutoff for the second bar is 83 in. 18 in.
101 in. or 8 ft 5 in. (37-in5-in18-in41-in
101-in.)
Note error it is 4-11 not 5-11
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Example Cutoff
The moment diagram is the blue line and the red
line is the envelope which encloses the moment
diagram.
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Bar Splices
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Tension Lap Splices
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Types of Splices
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Types of Splices
Class B Splice
(ACI 12.15.2)
All tension lay splices not meeting requirements
of Class A Splices
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Tension Lap Splice (ACI 12.15)
where As (reqd) determined for bending ld
development length for bars (not allowed
to use excess reinforcement modification
factor) ld must be greater than or
equal to 12 in.
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Tension Lap Splice (ACI 12.15)
Lap Splices shall not be used for bars larger
than No. 11. (ACI 12.14.2) Lap Splices should be
placed in away from regions of high tensile
stresses -locate near points of inflection (ACI
12.15.1)
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Compression Lap Splice (ACI 12.16)
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Compression Lap Splice (ACI 12.17.2)
In tied column splices with effective tie area
throughout splice length 0.0015 hs factor
0.83 In spiral column splices, factor 0.75
The final splice length must be 12 in.

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Example Splice Tension
Calculate the lap-splice length for 6 8 tension
bottom bars in two rows with clear spacing 2.5
in. and a clear cover, 1.5 in., for the following
cases
When 3 bars are spliced and As(provided)
/As(required) gt2 When 4 bars are spliced and
As(provided) /As(required) lt 2 When all bars are
spliced at the same location. fc 5 ksi
and fy 60 ksi
a. b. c.
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Example Splice Tension
For 8 bars, db 1.0 in and a b g l 1.0
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Example Splice Tension
The As(provided) /As(required) gt 2, class A
splice applies therefore lst 1.0 ld gt12 in.,
so lst 43 in. gt 12 in. The bars spliced are
less than half the number
The As(provided) /As(required) lt 2, class B
splice applies therefore lst 1.3 ld gt12 in.,
so lst 1.3(42.4 in.) 55.2 in. use 56 in. gt 12
in..
Class B splice applies and lst 56 in. gt 12 in.
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Example Splice Compression
Calculate the lap splice length for a 10
compression bar in tied column when fc 5 ksi and

• fy 60 ksi
• fy 80 ksi

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Example Splice Compression
For 10 bars, db 1.27 in.
Check ls gt 0.005 db fy 38.1 in. So ls 39 in.
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Example Splice Compression
For 10 bars, db 1.27 in. The ld 23 in.
Check ls gt (0.0009 fy 24) db
(0.0009(80000)-24)(1.27in.) 61 in. So use ls
61 in.