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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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F lexural Reinforcement in Slabs

For a 1 ft strip of slab is designed like a beam

As(reqd)is in units of (in2

/ft)

inchesinspacingbar

in12ft/ bs AA

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The table is A-9 from

MacGregors book.

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F lexural 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

7.6.5Sec.ACI

in.18

thicknessslab3tofsmaller

max

S

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F lexural Reinforcement in Slabs

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 tospan)

Maximum & Minimum reinforcement requirements

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F lexural Reinforcement in Slabs

Maximum & Minimum reinforcement requirements

T&S Reinforcement (perpendicular to span) ACI Sec 7.12

t

ftf

ft

ftA

*"12*0.0014

ksi60*"12*60*0018.0

ksi60*"12*0018.0

ksi50or40*"12*0020.0

y

y

y

ymins

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F lexural Reinforcement in Slabs

T&S Reinforcement (perpendicular to span) ACI Sec 7.12

Flexural Reinforcement (parallel to span) ACI Sec 10.54

Smaxfrom reinforced spacing

18"

5t

ofsmallermaxS

balsmaxs

&minsmins

75.0 AA

AA ST

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Reinforcement Development Lengths, Bar

Cutoffs, and Continuity RequirementsA. Concept of Bond Stress and Rebar Anchorage

Internal Forces in a beam

Forces in RebarBond stresses provide mechanism

of force transfer between concrete

and reinforcement.

Forces developed in the beam

by loading.

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Reinforcement Development Lengths, Bar

Cutoffs, and Continuity RequirementsEquilibrium Condition for Rebar

m= bond stress(coefficient of

friction)

Note: Bond stress is zero at cracks

m

m

4.

04

.

0ForceBond.0F

byd

bby

2

b

dfl

ldfd

T

bar

c

fk

fk

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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

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 infigure (b). Such splitting

comes largely from

wedging action when the

ribs of the deformed barbear 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 tothe yield strength, fy.

( ldused 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)

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 2dband

clear cover not less than db.

Other cases

No. 6 and smaller No. 7 and larger

bars and deformed barswires

c

y

b

d

25 f

f

d

l

c

y

b

d

20 f

f

d

l

c

y

b

d

50

3

f

f

d

l

c

y

b

d

40

3

f

f

d

l

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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.

5.2in which403

b

ct

b

ctc

y

b

d

dKc

d

Kcff

dl

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Factors used in expressions for

Development Length (ACI 12.2.4) 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

coating factor (epoxy prevents adhesion &

friction between bar and concrete.)Epoxy-coated bars or wires with cover less than 3dbor clear spacing less

than 6db

All other epoxy-coated bars or wires

Uncoated reinforcement

1.3

1.0

1.5

1.2

1.0

where < 1.7

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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 bars)

No.6 and smaller bars and deformed wire

No. 7 and larger bars

lightweight aggregate concrete factor (Reflects lowertensile strength of lightweight concrete, & resulting

reduction in splitting resistance.

When lightweight aggregate concrete is used.

However, when fctis specified, shall be permitted to be taken as

but not less than

When normal weight concrete is used

0.81.0

1.3

1.0

1.0

ctc7.6 ff

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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 ldin.

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.

ns

fAK

**1500

y ttr

tr

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Excess F lexural Reinforcement

Reduction (ACI 12.2.5)

Reduction = (Asreqd ) / (Asprovided )

- 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.

providedn

u

providedn

dreq'nReduction

M

M

M

M

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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

yb

c

yb

dbc

0003.0

0.02oflarger

fd

ffd

l

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Development Length for Bars in

Compression (ACI 12.3)Reduction Factors (ACI 12.3.3)

- Excessive Reinforcement Factor = (Asreqd)/(Asprovided)

- Spiral and Ties

If reinforcement is enclosed with spiralreinforcement 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

Noteldc< 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=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 whenthere 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 aredefined in ACI 7.1.

Hooks resists tension bybond 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.

.in6and8 wheresmultiplier* dbbdbhddh ldlll

Basic Development Length for Hooked Bar = lhb

when fy= 60,000 psi

c

bhd

1200

f

dl

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Design of Standard Hooks for

Tension Anchorage (ACI 12.5)

Conditions

Bar Yield StrengthBars with fyother 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 ReinforcementWhere anchorage or development for fy is not

specified required.

Lightweight Aggregate Concrete

Ties or StirrupsFor No. 11 bar and smaller.

Hook enclosed vertically or horizontally within ties

or stirrup-ties spaced along full ldhno farther apart

than 3db, where dbis 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 ReinforcementHooked bars with epoxy coating

Multiplier

1.2

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Example

Determine the

anchorage of 4 #8 top

bars in column. Thetransverse steel is 4#11.

fy= 60000 psi

fc= 3000 psi