# Lecture 19 - Bar Development

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```					Lecture 19 - Bar Development

October14, 2002
CVEN 444
Lecture Goals
• Slab design reinforcement
• Bar Development
• Hook development
Flexural Reinforcement in Slabs
For a 1 ft strip of slab is designed like a beam
As (req’d) is in units of (in2/ft)

        12 in          
As / ft  Ab                        
 bar spacing in inches 
The table will allow
to determine the
amount of steel per
each foot of slab.
Flexural Reinforcement in Slabs
The minimum spacing of the bars is given as:

3t slab thickness
Smax  smaller of                         ACI Sec.7.6.5
       18 in.

Also, check crack control - important for exterior exposure
(large cover dimensions) - The spacing S of reinforcement
closest to the surface in tension ACI Sec. 10.6.4

540           12  36 
s      2.5cc 
fs              fs
Flexural Reinforcement in Slabs
Maximum & Minimum reinforcement requirements
• Thin slabs shrink more rapidly than deeper beams.

• Temperature & shrinkage (T&S) steel is provided
perpendicular to restrain cracks parallel to span.
(Flexural steel restrains cracks perpendicular to
span)
Flexural Reinforcement in Slabs
Maximum & Minimum reinforcement requirements
T&S Reinforcement (perpendicular to span) ACI Sec 7.12.2

As min  0.0020 * 12"* t         f y  40 or 50 ksi
 0.0018* 12"* t            f y  60 ksi
 60 
 0.0018*   * 12"* t      f y  60 ksi
f 
 y
 0.0014* 12 "* t
Flexural Reinforcement in Slabs
T&S Reinforcement (perpendicular to span) ACI Sec
7.12.2.2

 5t
S max  smaller of 
18"
t – thickness of the slab
Flexural Reinforcement in Slabs
Flexural Reinforcement (parallel to span) ACI Sec 10.5.4

As min   Asmin T &S
 3t
Smax    smaller of 
18"
Smax from reinforced spacing
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
A. Concept of Bond Stress and Rebar Anchorage
Internal Forces in a beam
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
A. Concept of Bond Stress and Rebar Anchorage
Forces in Rebar
Bond stresses provide mechanism of force transfer
between concrete and reinforcement.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
Equilibrium Condition for Rebar

 F  0.  T  Bond Force 0               = bond stress
 d b2                        (coefficient of
.             f y   d blb   0 friction)  k     fc
4
f ydb                        k  f bar 
.  ld 
4
Note: Bond stress is zero at cracks
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
Sources of Bond Transfer
(1) Adhesion between concrete & reinforcement.
(2) Friction
Note: These properties are quickly lost for tension.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
(3)Mechanical Interlock.
The edge stress concentration causes cracking to
occur.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
(3) Mechanical Interlock (cont).
Force interaction between the steel and concrete.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements

Splitting cracks result in loss of bond transfer.
Reinforcement can be used to restrain these
cracks.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
1. Minimum edge distance and spacing of bars
( smaller distance = smaller load )
2. Tensile strength of concrete.
3. Average bond stress along bar. ( Increase in
bond stress     larger wedging forces. )
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
Typical Splitting Failure Surfaces.
Reinforcement Development Lengths, Bar
Cutoffs, and Continuity Requirements
Typical Splitting Failure Surfaces.
Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
General splitting of
concrete along the
bars,either in vertical
planes as in figure (a) or
in horizontal plane as in
figure (b). Such splitting
comes largely from
wedging action when the
ribs of the deformed bar
bear against the concrete.
The horizontal type of splitting frequently begins at a diagonal
crack. The dowel action increases the tendency toward splitting.
This indicates that shear and bond failure are often intricately
interrelated.
Reinforcement Development Lengths
B. ACI Code expression for development length for
bars in tension/in compression.
Development Length, ld
Shortest length of bar in which the bar stress can
increase from zero to the yield strength, fy.
( ld used since bond stresses, , vary along a bar in
a tension zone)
Reinforcement Development Lengths
Development Length, ld

( ld used since bond
stresses, , vary along a
bar in a tension zone)
Development Length for Bars in Tension
Development length, ld  12” ACI 12.2.1
fc  10000 psi for Ch. 12 provisions for development length in ACI Codes.

Development length, ld (simplified expression from ACI 12.2.2)
No. 6 and smaller No. 7 and larger
bars and deformed bars
wires
Clear spacing of bars being developed or
spliced not less than db, clear cover not less
than db, and stirrups or ties throughout ld not    ld   f y       ld   f y
less than the code minimum                                             
or                             d b 25 f c        d b 20 f c
Clear spacing of bars being developed or
spliced not less than 2db and clear cover not           38               47.5
less than db.
Development Length for Bars in Tension
Development length, ld  12” ACI 12.2.1
fc  10000 psi for Ch. 12 provisions for development length in ACI Codes.

Development length, ld (simplified expression from ACI 12.2.2)
No. 6 and smaller No. 7 and larger
bars and deformed bars
wires
Other cases                            ld 3 f y         ld 3 f y
                   
d b 50 f c          d b 40 f c

57               71

fc = 4 ksi fy = 60 ksi , ,,  1.0
Development Length for Bars in Tension
Development length, ld     ACI 12.2.3

ld   3 fy                      c  K ct 
                              d   2.5
in which           
d b 40 f c  c  K ct                     

 d                       b

     b    
2.5 limit to safeguard against pullout type failure.
Factors used in expressions for
Development Length (ACI 12.2.4)
  reinforcement location factor            where  < 1.7

Horizontal reinforcement so placed that
more than 12 in of fresh concrete is cast         1.3
in the member below the development
length or splice
Other reinforcement                               1.0
Factors used in expressions for
Development Length (ACI 12.2.4)
  coating factor (epoxy prevents adhesion &
friction between bar and concrete.)
Epoxy-coated bars or wires with cover less        1.5
than 3db or clear spacing less than 6db
All other epoxy-coated bars or wires              1.2
Uncoated reinforcement                            1.0

where  < 1.7
Factors used in expressions for
Development Length (ACI 12.2.4)
g  reinforcement size factor (Reflects more favorable
performance of smaller 
bars)
No.6 and smaller bars and deformed wire        0.8
No. 7 and larger bars                          1.0
Factors used in expressions for
Development Length (ACI 12.2.4)
  lightweight aggregate concrete factor (Reflects
lower tensile strength of lightweight concrete, &
resulting reduction in splitting resistance.)
When lightweight aggregate concrete is used.       1.3
However, when fct is specified, shall be           1.0
permitted to be taken as 6.7 f c f ct but not
less than
When normal weight concrete is used                1.0
Factors used in expressions for
Development Length (ACI 12.2.4)
c = spacing or cover dimension, in.
Use the smaller of either
(a) the distance from the center of the bar or wire to
the nearest concrete surface.
or
(b) one-half the center-to-center spacing of the bar or
wires being developed.
Factors used in expressions for
Development Length (ACI 12.2.4)
Ktr = transverse reinforcement index (Represents the
contribution of confining reinforcement across
potential splitting planes.)

Atr f y t
K tr 
1500 * s * n
Factors used in expressions for
Development Length (ACI 12.2.4)
Atr =   Total cross-section area of all transverse
reinforcement within the spacing s, which
crosses the potential plane of splitting along
the reinforcement being developed with in the
development length, in2.
fyt =   Specified yield strength of transverse
reinforcement, psi.
Factors used in expressions for
Development Length (ACI 12.2.4)
s = maximum center-to-center spacing of
transverse reinforcement within ld in.
n = number of bars or wires being developed
along the plane of splitting.

Note: It is permitted to use Ktr = 0 as a design
simplification even if transverse reinforcement is
present.
Excess Flexural Reinforcement
Reduction (ACI 12.2.5)
Reduction = (As req’d ) / (As provided )
- Except as required for seismic design (see ACI
21.2.1.4)
- Good practice to ignore this provision, since use
of structure may change over time.
- final ld  12 in.                                Mu
M n req'd             
Reduction                      
M n provided       M n provided
Development Length for Bars in
Compression (ACI 12.3)
Compression development length,
ldc = ldbc * applicable reduction factors  8 in.
Basic Development Length for Compression, ldbc
 0.02 d b f y

ldbc    larger of       fc
0.0003 d b f y

Development Length for Bars in
Compression (ACI 12.3)
Reduction Factors (ACI 12.3.3)
- Excessive Reinforcement Factor = A( s req’d ) / A( s provided)
- Spiral and Ties
If reinforcement is enclosed with spiral
reinforcement  0.25 in. diameter and  4 in.
pitch or within No. 4 ties according to 7.10.5 and
spaced  4 in. on center. Factor = 0.75
Development Length for Bars in
Compression (ACI 12.3)
Reduction Factors (ACI 12.3.3)
Note
ldc < ld (typically) because
- Beneficial of end bearing is considered
- weakening effect of flexural tension cracks is
not present for bars in compression.
Hooked Bar at Discontinuous
Ends (ACI 12.5.4)
If side cover and top (or bottom cover)  2.5 in. Enclose
hooked bar w/ ties or stirrup-ties:

Spacing  3db
db = of hooked bar

Note: Multiplier for ties or
stirrups (ACI 12.5.3)
is not applicable for
this case.
Hooked Bar at Discontinuous
Ends (ACI 12.5.4)
- Basic Development lengths

Others     Mechanical Anchorage   ACI (12.6)
Welded Wire Fabric     ACI (12.7)
Bundled Bars           ACI (12.4)
Standard Hooks for Tension Anchorage

C. Use of Standard Hooks for Tension Anchorage
there is insufficient length available to
develop a bar.
Note: Hooks are not allowed to developed compression
reinforcement.
Standard Hooks for Tension Anchorage

Standard Hooks are
defined in ACI 7.1.

Hooks resists tension by
bond stresses on bar
surface and bearing on on
concrete inside the hook.
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Development Length for Hooked Bar, ldb.
ldh  lhd * multiplier s   where ldb  8 d b and ldb  6 in .

Basic Development Length for Hooked Bar = lhd
when fy = 60,000 psi
lhd 1200

db    fc
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Conditions                                Multiplier
Bar Yield Strength Bars with fy other      fy /60,000
than 60,000 psi
Concrete Cover for 180 Degree Hooks
For No. 11 bars and smaller. Side cover       0.7
(normal to plane of hook)  2.5 in.
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Conditions                                  Multiplier

Concrete Cover for 90 Degree Hooks
For No. 11 bars and smaller. Side cover
(normal to plane of hook)  2.5 in. Cover       0.7
on bar extension beyond hook tail  2 in.
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Conditions                          Multiplier
Excessive Reinforcement             As(req’d) /
Where anchorage or development      As(provided)
for fy is not specified required.

Lightweight Aggregate Concrete           1.3
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Conditions                                  Multiplier
Ties or Stirrups
For No. 11 bar and smaller.
Hook enclosed vertically or horizontally
within ties or stirrup-ties spaced along        0.8
full ldh no farther apart than 3db, where
db is diameter of hooked bar.
Design of Standard Hooks for
Tension Anchorage (ACI 12.5)
Conditions                       Multiplier

Epoxy-coated Reinforcement           1.2
Hooked bars with epoxy coating
Example
Determine the
anchorage of 4 #8
top bars in column.
The transverse steel
is 4#11.
fy = 60000 psi
fc = 3000 psi

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