DevelopmentLength.08.ppt

8/14/2019 DevelopmentLength.08.ppt

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Development Length

CE A433RC Design

T. Bart Quimby, P.E., Ph.D.Revised Spring 2009


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Consider a bar embedded in a

mass of concrete

P = t*[Lb*p*db]

P = s* [p*db2/4]

t= P / [Lb*p*db] < tmax

P < tmax* [Lb*p*db]

s = P/ [p*db2/4] < smax

P < smax* [p*db2/4]

To force the bar to be the weak link: tmax* [Lb*p*db] > smax* [p*db2/4]

Lb> (smax/ tmax)* [db/4]

Lb

db


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Development Length Ld= development length

the shortest distance over which a bar can achieve itsfull capacity

The length that it takes a bar to develop its full

contribution to the moment capacity, Mn

Cc

Ts

Mn= (C or T)*(dist)

Mn

0

Ld


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Steel Limit, smax

Using the bilinear assumption of ACI 318:

smax= + fy

Lb> (fy/ tmax)* [db/4]

Lb> fy* db/ (4*tmax)


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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 theconcrete

The presence of transverse steel


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Concrete Strength, fc

Bond strength, tmax, tends to increase withconcrete strength.

Experiments have shown this relationshipto be proportional to the square root of fc.


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Amount of Concrete Below Bars

The code refers to topbars as being any barwhich has 12 inches or

more of fresh concretebelow the bar when themember is poured.

If concrete > 12 then

consolidation settlementresults in lower bondstrength on the bottom sideof the bar

See ACI 318-08, 12.2.4(a)


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Surface Condition of Rebar

All rebar must meet ASTM requirementsfor deformations that increase pulloutstrength.

Bars are often surface coated is inhibitcorrosion. 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 toeach bar is used to account for proximity ofsurfaces or other bars.

2D 3D
http://localhost/var/www/apps/conversion/tmp/scratch_11/DevLen01.dwghttp://localhost/var/www/apps/conversion/tmp/scratch_11/DevLen3D.dwghttp://localhost/var/www/apps/conversion/tmp/scratch_11/DevLen3D.dwghttp://localhost/var/www/apps/conversion/tmp/scratch_11/DevLen3D.dwghttp://localhost/var/www/apps/conversion/tmp/scratch_11/DevLen01.dwg


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Presence of Transverse Steel

The bond transfer tends to cause a splitting plane

Transverse steel will increase the strength of thesplitting plane.

See text for other possible splitting locations


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The ACI 318-08 Development

Length Equation (ACI 318-08 12.2)

b

b

trb

set

c

y

d d

d

Kcf

fL

5.2,min

)7.1,min(

40

3

l

sn

AK trtr

40


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More Modifiers

s, Modifier for bar size

0.8 for #6 and smaller

1.0 for #7 and larger

l, Modifier for lightweight concrete

ACI 318-08, 8.6.1

l = 1.0 for normal weight concrete

las low as 0.75 for the lightest weightconcrete


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The Transverse Reinforcement

Index, Ktr (ACI 318-08 Eq. 12-2) Atr= total cross sectional area of

all transverse reinforcement whichis within the spacing, s, and whichcrosses the potential plane ofsplitting through thereinforcement being developed.

s = maximum C-C spacing oftransverse reinforcement withinthe development length

n = number of longitudinal barsbeing developed along the planeof splitting.

sn

AK trtr

40


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The outer bars are #10, the center one is #6, the others are #8


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Other Development Lengths

Development in Compression: ACI 318-0812.3

Development of standard hooks intension: ACI 318-08 12.5 There are some very specific cover and/or

confinement requirements

Mechanical connectors (such as bearingplates at the beam ends) may also beused.


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Moment Capacity Diagram

Moment Capacity

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X (in)

phiPm(

ft-k)


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Cutting Bars

The fMndiagram can be made to more closelyfit the Mudiagram by terminating or cutting barswhen they are no longer needed. (ACI 318-0812.10.3)

Moment Capacity

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400

X (in)

phiPm

(ft-k) End of #6 bar

End of #8 bars

End of #10 bars

> max(d, 12db)

> max(d, 12db)


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Beam Profile Showing Bar Cutoff

Locations

Documents

DevelopmentLength.08.ppt