Lecture 14 Design

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Lecture 14 - Design

• October 18, 2001
• CVEN 444

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Lecture Goals

• Slab design reinforcement
• Bar Development
• Hook development

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Flexural Reinforcement in Slabs
For a 1 ft strip of slab is designed like a beam
As(reqd) is in units of (in2/ft)
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The table is A-9 from MacGregors book.
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Flexural Reinforcement in Slabs
The minimum spacing of the bars is given as
Also, check crack control - important for
exterior exposure (large cover dimensions) - ACI
Sec. 10.6.4
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Flexural Reinforcement in Slabs
Maximum Minimum reinforcement requirements

• Thin slabs shrink more rapidly than deeper beams.
• Temperature shrinkage (TS) steel is provided
  perpendicular to restrain cracks parallel to
  span. (Flexural steel restrains cracks
  perpendicular to span)

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Flexural Reinforcement in Slabs
Maximum Minimum reinforcement requirements
TS Reinforcement (perpendicular to span) ACI Sec
7.12
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Flexural Reinforcement in Slabs
TS Reinforcement (perpendicular to span) ACI
Sec 7.12
Flexural Reinforcement (parallel to span) ACI
Sec 10.54
Smax from reinforced spacing
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
A. Concept of Bond Stress and Rebar Anchorage
Internal Forces in a beam
Forces developed in the beam by loading.
Forces in Rebar
Bond stresses provide mechanism of force transfer
between concrete and reinforcement.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
Equilibrium Condition for Rebar
m bond stress (coefficient of friction)
Note Bond stress is zero at cracks
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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.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
Sources of Bond Transfer
(3)Mechanical Interlock.
The edge stress concentration causes cracking to
occur.
Force interaction between the steel and concrete.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
Splitting cracks result in loss of bond transfer.
Reinforcement can be used to restrain these
cracks.
Splitting Load is Affected by
Minimum edge distance and spacing of bars
(smaller distance smaller load) Tensile strength
of concrete. Average bond stress along
bar.(Increase in bond stress
larger wedging forces)
1. 2. 3.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
Typical Splitting Failure Surfaces.
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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.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
ACI Code expression for development length for
bars in tension/in compression.
B.
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, m, vary along
a bar in a tension zone)
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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 less than
the code minimum or Clear spacing
of bars being developed or spliced not less than
2db and clear cover not less than db. Other cases
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Development Length for Bars in Tension
Development length, ld ACI 12.2.3
2.5 limit to safeguard against pullout type
failure.
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Factors used in expressions for Development
Length (ACI 12.2.4)
where ab lt 1.7
a reinforcement location factor
Horizontal reinforcement so placed that more than
12 in of fresh concrete is cast in the member
below the development length or splice Other
reinforcement
1.3 1.0
b coating factor (epoxy prevents adhesion
friction between bar and concrete.)
Epoxy-coated bars or wires with cover less than
3db or clear spacing less than 6db All other
epoxy-coated bars or wires Uncoated reinforcement
1.5 1.2 1.0
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Factors used in expressions for Development
Length (ACI 12.2.4)
g reinforcement size factor (Reflects more
favorable performance of
smaller f bars)
No.6 and smaller bars and deformed wire No. 7 and
larger bars
0.8 1.0
l lightweight aggregate concrete factor
(Reflects lower
tensile strength of lightweight concrete,
resulting reduction in splitting resistance.
1.3 1.0 1.0
When lightweight aggregate concrete is
used. However, when fct is specified, shall be
permitted to be taken as but not
less than When normal weight concrete is used
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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.
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Factors used in expressions for Development
Length (ACI 12.2.4)
Kct transverse reinforcement index (Represents
the contribution of confining reinforcement
across potential splitting planes.)
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. Specified yield strength
of transverse reinforcement, psi. maximum
center-to-center spacing of transverse
reinforcement within ld in. number of bars or
wires being developed along the plane of
splitting.
Atr
fyt s n
Note It is permitted to use Kct 0 as a design
simplification even if transverse reinforcement
is present.
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Excess Flexural Reinforcement Reduction (ACI
12.2.5)
Reduction (As reqd ) / (As provided )
- Except as required for seismic design (see ACI
21.2.14) - Good practice to ignore this
provision, since use of structure may change over
time. - final ld 12 in.
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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
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Development Length for Bars in Compression (ACI
12.3)
Reduction Factors (ACI 12.3.3)
- Excessive Reinforcement Factor (As reqd)/(As
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
Note ldc lt ld (typically) because - Beneficial
of end bearing is considered - weakening effect
of flexural tension cracks is not present
for bars in compression.
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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 f of hooked bar
Note Multiplier for ties or stirrups (ACI
12.5.3.3) is not applicable for this case.
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Hooked Bar at Discontinuous Ends (ACI 12.5.4)
Table A-11, A-12, A-13 (Back of textbook) - Basic
Development lengths
Others
Mechanical Anchorage ACI (12.6) Welded Wire
Fabric ACI (12.7) Bundled Bars ACI (12.4)
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
C. Use of Standard Hooks for Tension Anchorage
Hooks provide additional anchorage when there is
insufficient length available to develop a bar.
Note Hooks are not allowed to developed
compression reinforcement.
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Reinforcement Development Lengths, Bar Cutoffs,
and Continuity Requirements
C. Use of 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.
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Design of Standard Hooks for Tension Anchorage
(ACI 12.5)
Development Length for Hooked Bar, ldb.
Basic Development Length for Hooked Bar lhb
when fy 60,000 psi
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Design of Standard Hooks for Tension Anchorage
(ACI 12.5)
Conditions Bar Yield Strength Bars with
fy other than 60,000 psi Concrete Cover for 180
Degree Hooks For No. 11
bars and smaller. Side cover
(normal to plane of hook) 2.5 in. Concrete
Cover for 90 Degree Hooks
For No. 11 bars and smaller.
Side cover (normal to plane of hook) 2.5 in.
Cover on bar extension beyond hook tail 2 in.
Multiplier fy /60,000 0.7 0.7
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Design of Standard Hooks for Tension Anchorage
(ACI 12.5)
Conditions Excessive Reinforcement
Where anchorage or development for fy is not
specified required. Lightweight Aggregate
Concrete Ties or
Stirrups For No. 11 bar
and smaller. Hook
enclosed vertically or horizontally within ties
or stirrup-ties spaced along full ldh no farther
apart than 3db, where db is diameter of hooked
bar.
Multiplier As(reqd) / As(provided) 1.3 0.8
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Design of Standard Hooks for Tension Anchorage
(ACI 12.5)
Conditions Epoxy-coated Reinforcement
Hooked bars with epoxy coating
Multiplier 1.2
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Example
Determine the anchorage of 4 8 top bars in
column. The transverse steel is 411. fy
60000 psi fc 3000 psi