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Lecture on
CE 4014
Design of Concrete Structures
Yangon Technological University
Department of Civil Engineering
Dr. Khin Than YuProfessor and Head
(Bond, Anchorage and Development Length)
Part (I)
20-3-2008
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Department of CivilEngineering, YTU 2
Design of Concrete Structures
Text and Reference
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Department of CivilEngineering, YTU 3
FUNDAMENTALS OF FLEXURAL BOND
In reinforced concrete beamsit is assumed that strain in theembedded reinforcing bar isthe same as that in thesurrounding concrete.
Therefore, it is essential thatbond force is developed on theinterface between concreteand steel to prevent significantslip from occurring at theinterface.
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Source of bond strength
Weak chemical adhesion Mechanical friction between
steel and concrete Slip induced interlocking of
natural roughness of the bar
with concrete End anchorage, hooks :
providing tie arch actioneven for bond broken beam.
Force in the steel,T = Mmax / z
Deformed bar: providing bondforce via the shoulders of theprojecting ribs bear on thesurrounding concrete.
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a. Bond Stress Based on Simple
Cracked Section Analysis
dT = dM / jdFor local equi l ibr ium ,
change in
bar force = bon d force
at the contact
surface
u o dx = dT,
u= dT/
o dx
= dM / o
jd dx
= dV / ojd
u = local average unit bond stress
o = sum of the per imeter of al l bars
Jd = internal lever arm between tensile
and compressive force resultants
dx = sho rt piece of length o f beam
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b. Actual Distribution of Flexural Bond
Stress
Pure bending case Concrete fails to resist tensile
stresses only where the actualcrack is located. Steel T ismaximum and
Tmax = M / jd . Between cracks , concrete does
resist moderate amount of tensionintroduced by bond.
uis proportional to the rate ofchange of bar force, and highestwhere 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 cracksectional theory, T isproportional to the momentdiagram and u is proportionalto shear force diagram.
In actual, T is less than thesimple analysis predictioneverywhere except at theactual cracks.
Similarly, u is equal withsimple analysis prediction only
at the location where slopes ofthe steel force diagrams areequals .If the slope is greaterthan assumed, bond stress isgreater; if the slope is lessbond stress is less.
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ULTIMATE BOND STRENGTH AND
DEVELOPMENT LENGTH
Types of bond failure
Direct pulloutof bars(small diameter bars are
used with sufficientlylarge concrete coverdistances and barspacing)
Splitting of theconcretealong the bar
(cover or bar spacing isinsufficient to resist thelateral concrete tensionresulting from thewedging effect of bardeformations)
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a. 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 ofthe bar deformation and bar pullout results. 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 adjacent to cracks leads to this failure below the failure load of thebeam. 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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b. Development Length
Development lengthis the length of embedment necessary to developthe full tensile strength of bar, controlled by either pullout or splitting.
In Fig., let
maximum M at a and zero at support fs at aT = Abfs _
Development length concepttotal tension force must betransferred from the bar to the concrete in the distance l bybond stress on the surface.
To fully develop the strength T = Abfy
ld , development length
Safety against bond failure: the length of the bar from any point ofgiven steel stress to its nearby end must be at least equal to itsdevelopment length. If the length is inadequate, special anchorage canbe provided.
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c. Factors influencing Development
Length
Tensile strength of concrete
Cover distance
Bar spacing
Lateral reinforcement
Vertical bar location relative to beam depth
Epoxy coated bars or not
Excess reinforcement
Bar diameter
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ACI CODE PROVISION FOR DEVELOPMENT
OF TENSION REINFORCEMENT
Limit (c + k
tr) / d
b= 2.5 for
pullout case
fc are not to begreater than 100 psi.
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For two cases of practical importance, using (c + ktr) /
db= 1.5,
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Example:
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Continue:
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Continue:
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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.
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b. Development Length and Modification
Factors for Hooked Bars
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Example
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ANCHORAGE REQUIREMENTS FOR WEB
REINFORCEMENT
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DEVELOPMENT OF BARS IN
COMPRESSION
Reinforcement may berequired to develop itscompressive strength by
embedment under variouscircumstances.
ACI basic developmentlength in compression
ldb= 0.02dbfy/fc
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BAR CUTOFF AND BEND POINTS IN BEAMS
Theoretical points of cutoff orbend
T = As fs = M/z
T = function of (M)
ACI Code: uniformly loaded,continuous beam of fairly regularspan may be designed usingmoment coefficients.
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b. Practical Considerations and ACI Code
Requirements
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If cutoff points are in tension zone (to preventformation of premature flexural and diagonal
tension cracks) no flexural bar shall be terminatedunless the following conditions are specified.
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Standard Cutoff
and BendPoints
For not more
than 50% oftensile steel isto be cutoff orbent
S i l R i h P i
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c. Special Requirements near the Point
of Zero Moment
It is necessary to consider whenever the moments over thedevelopment length are greater than those corresponding toa linear reduction to zero.
Bond force per unit length , u = dT / dx = dM / zdx,
proportional to the slope of the moment diagram. Maximum bond forces u would occur at point of inflection
and pullout resistance is required.
Slope of M diagram at any point = V at that point
Let Mn = nominal flexuralstrength provided by those
bars extend to the
point of inflection.
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For assumed (conservatively) uniformed slope of momentdiagram Vutowards the positive moment region, length aatM = Mn
a= Mn/Vu
Thus a must be greater than or equal to ld
ACI Code
Simply support case
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d. Structural Integrity Provisions
For major supporting elements, such as columns, totalcollapse can be prevented through relatively minorchanges in bar detailing owing to accidental or abnormalloading.
If some reinforcement properly confined is carriedcontinuously through a support catenary action of beamcan prevent from total collapse even if the support isdamaged.
ACI Code
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Comment
Consideration for bond and detail designfor anchorage, development length andstructural integrity requirements are
important to have proper structuralperformance of the building.