CE 419 Lec 1 Bond and Developement Length

8/18/2019 CE 419 Lec 1 Bond and Developement Length

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CE 419Plain and Reinforced Concrete III

NUST Institute of Civil Engineering

(Bond, Anchorage and Development Length)

Fall 2012

Dr. Wasim Khaliq


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Design of Concrete Structures

Text and Reference


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Fundamentals of Flexural Bond

In reinforced concrete beams it isassumed that strain in theembedded reinforcing bar isthe same as that in thesurrounding concrete.

Therefore, it is essential that bondforce is developed on theinterface between concrete and

steel to prevent significant slipfrom occurring at the interface.


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Source of Bond Strength

• Weak chemical adhesion

• Mechanical friction between steeland concrete

• Slip induced interlocking of naturalroughness of the bar with concrete

• End anchorage, hooks : providingtie arch action even for bondbroken beam.

Force in the steel,

T = M max

/ jd

• Deformed bar: providing bondforce via the shoulders of theprojecting ribs bear on thesurrounding concrete.


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Bond Stress Based on Simple Cracked Section Analysis

dT = dM / jd

For local equilibrium,change in bar force = bond

force at the contact surface

U dx = dT,

U = dT / dx

= dM / jd dx

U = dV / jd

* Elastic crack equation

U = local average unit bond stress

jd = internal lever arm between tensileand compressive force resultants

dx = short piece of length of beam


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Actual Distribution of Flexural Bond Stress

Pure bending case

– Concrete fails to resist tensilestresses only where the actual crack

is located. Steel T is maximum and

T max = M / jd

– Between cracks , concrete doesresist 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 forcecurve is greatest.

– Very high local bond stress adjacent

to the crack.


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Beam under transverse loads,

– According to simple crack sectionaltheory, T is proportional to the moment

diagram and U is proportional to shearforce diagram.

– In actual, T is less than the simple

analysis prediction everywhere except at

the actual cracks.

– Similarly, U is equal with simple analysisprediction only at the location where

slopes of the steel force diagrams areequals. 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 usedwith sufficiently large concrete

cover distances and bar spacing)

– Splitting of the concretealong the bar (cover or barspacing is insufficient to resist thelateral concrete tension resultingfrom the wedging effect of bardeformations)


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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 pulloutresults.

• 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 adjacentto 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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Development Length

• Development length is the length of embedment necessary to develop thefull tensile strength of bar, controlled by either pullout or splitting.

• In Fig., let

– maximum M at a and zero at support

– fs at a is T = Ab f s

• Development length concepttotal tension force must betransferred from the bar to the concrete in the distance ‘l ’ by bondstress on the surface.

•To fully develop the strength of bar

T = Ab f y the distance

‘l

’mustbe equal to ‘l d ’ = development length

• Safety against bond failure: the length of the bar from any point of givensteel stress to its nearby end must be at least equal to its developmentlength. If the length is inadequate, special anchorage such as hooks must

be provided.


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Factors influencing Development Length

• Tensile strength of concrete

• Cover distance

• Bar spacing

• Lateral reinforcement

• Vertical bar location relative to beam depth (bond strength reducedwith placement of bars higher from bottom)

• Epoxy coated bars or not (bond strength reduced dut to reduced

friction of epoxy coating)

• Excess reinforcement

• Bar diameter (smaller diameter bars need lower development

length


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Factors influencing Development Length

Cover distance and bar spacing

Transvers reinforcement


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ACI Code Provision for Development of Tension Reinforcement

Limits (c + k tr) / db > 2.5 pullout failure

(c + k tr) / db < 1.5 splitting failure

√ f’c are not to be greater than

100 psi.


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For two cases of practical importance, use (c + k tr ) / d b = 1.5 ,

Simplified Equations for Development Length


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Further Simplification for Development Length


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Further Simplification for Development Length


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Example


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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 . [ ACI 7.1]


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Anchorage of Tension Bars by Hooks

For stirrup and tie hooks, for bar sizes #5 and smaller, the inside

diameter should not be less than 4 bar diameters – ACI Code


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Development Length and Modification Factors for Hooked Bars

l dh

is measured from critical section to farthest point

on the bar parallel to straight part of the bar and is:


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l dh must be

modified byapplicable

modification

factors::


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Requirements for Transverse Reinforcement

Transverse Steel Essential:

• When hooks required at the ends of SS beam

• Discontinuous end of beam with small cover

distance like ending at column

• Bars anchored in a short cantilever


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ExampleDevelopment of hooked bars in tension. Referring to the beam-column joint shown,

No. 11 (No. 36) negative bars are to be extended into the column and terminated in a

standard 90° hook, keeping 2 in. clear to the outside face of the column. The columnwidth in the direction of beam width is 16 in. Find the minimum length of embedment of

the hook past the column face, and specify the hook details


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Example

Excess rft: Asreq /Asprovided=2.9/3.12=0.93

A h R i t f


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Anchorage Requirements for

Web Reinforcement


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Problem 5.1


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Diameters and Areas of Standard Rebars

F t d L d C bi ti ACI 318 08


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Factored Load Combinations – ACI 318-08


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D l f B i C i


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Development of Bars in Compression

ACI basic development length incompression is greater of

I

Hooks as used for tension reinforcement are not effective in transferring

compression from bars to concrete and should be disregarded in

determining required embedment length.


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Development of Bars in Compression

Modification in Compressive l dc

l dc is not to be less than 8″


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Basic and Modified

Compressive l dc

as per ACI 12.3


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Bar Cutoff and Bend Points in Beams

Theoretical points of cutoff or

bend

T = As f s = M/z

T = function of (M)

ACI Code: uniformly loaded,

continuous beam of fairly regularspan may be designed using

moment coefficients.

To determine cutoff points for

continuous beams, M diagram frommax span M and max support M are

drawn


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Bar Cutoff and Bend Points in Beams100

90

80

70

60

50

40

30

20

10

0

M o m e n t ( M

u )

B C t ff d B d P i t i C ti B


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Bar Cutoff and Bend Points in Continuous Beams


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100


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100

90

80

70

60

50

40

30

20

10

0

M o m e n t ( M

u )


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If cutoff points are in tension zone (to prevent

formation of premature flexural and diagonaltension cracks) no flexural bar shall be terminatedunless the following conditions are specified.


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• Standard Cutoff and Bend Points

• For not more than 50% of tensile steel is to be cutoff or bent

Special Requirements near the Point of Zero Moment


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Special Requirements near the Point of Zero Moment

It is necessary to consider whenever the moments over the development length aregreater than those corresponding to a linear reduction to zero.

Bond force per unit length , u = dT / dx = dM / zdx , proportional to the slope of themoment diagram.

Maximum bond forces u would occur at point of inflection and pullout resistance isrequired.

Slope of M diagram at any point = V at that point

Let Mn = nominal flexural

strength provided by thosebars extend to the

point of inflection.


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For assumed (conservatively) uniformed slope of moment

diagram Vu towards the positive moment region, length a at M= Mn

a = M n /V u

Thus a must be greater than or equal to l d

ACI Code

•Simply support case

Structural Integrity Provisions


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Structural Integrity Provisions

• For major supporting elements, such as

columns, total collapse can be preventedthrough relatively minor changes in bar detailingowing to accidental or abnormal loading.

• If some reinforcement properly confined iscarried continuously through a support catenaryaction of beam can prevent from total collapseeven if the support is damaged.

• ACI Code 7.13.2

Structural Integrity


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g yProvisions

Lap Splices


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• Supplied Lengths

– Bar # 5 - # 18 – 60 ft

– Bar # 4 and below – 20 to 40 ft

Lap Splices

• Splices at points of maximum stress should be avoided

• When used splices should be staggered

• For #11 and smaller bars simple lapping of bars is made to a

sufficient distance to transfer stress by bond

• Lapped bars a placed in contact and lightly wire bound

• Alternate way is welding and mechanical devices

• ACI does not allow lapped splices for > #11 bars• Except that #14 and #18 bars may be splice in compression with

#11 and smaller bars

Lap Splices in Tension


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Lap Splices in Tension

• Stated in terms of development length - l d

• For calculation of l d , the usual modification factors may beapplied but NOT the excess steel modification factor

• Classification of lap splices in tension (based on minimum length

of lap required)

– Class A lap splices – 1.0 l d but not less than 12 in

– Class B lap splices – 1.3 l d but not less than 12 in

Lap Splices in Compression


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Lap Splices in Compression

• Mainly used in columns• Bars in columns are generally terminated just above each floor

– Due to construction convenience – avoid handling long column bars

– To permit column steel area to reduce in steps


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Comment

• Consideration for bond and detail design for

anchorage, development length and structural

integrity requirements are important to have proper

structural performance of the building.


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As a design simplification, it is conservative to assume

Ktr = 0, even if the transverse reinforcement is present. theterm (c + Ktr ) / db in the denominator of accounts for the

effects of small cover, close bar spacing and confinement

provided by transverse reinforcement. The ACI codegives simplified versions of eqn 5.4 for preselected values

of (c + Ktr ) / db. However, the development length ld

computed by eqn 5.4 is mostly substantially shorter thandevelopment length computed from simplified eqns.

CE 419 Lec 1 Bond and Developement Length

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